{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/tpq_logo.png\" alt=\"The Python Quants\" width=\"35%\" align=\"right\" border=\"0\"><br><br><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Listed Volatility and Variance Derivatives\n",
    "\n",
    "**Dr. Yves J. Hilpisch &mdash; Wiley Finance (2016)**\n",
    "\n",
    "<img src=\"http://hilpisch.com/images/lvvd_cover.png\" alt=\"Derivatives Analytics with Python\" width=\"30%\" align=\"left\" border=\"0\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Realized Variance and Variance Swaps"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introdution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Realized Variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "@suppress\n",
    "import warnings; warnings.simplefilter('ignore')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "## text/csv file containing daily closing levels of EURO STOXX 50 index\n",
    "path = 'https://www.stoxx.com/document/Indices/Current/HistoricalData/'\n",
    "es_url = path + 'hbrbcpe.txt'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "## column names for the data set\n",
    "cols = ['Date', 'SX5P', 'SX5E', 'SXXP', 'SXXE',\n",
    "        'SXXF', 'SXXA', 'DK5F', 'DKXF', 'DEL']\n",
    "try: # reading the data with pandas\n",
    "    es = pd.read_csv(es_url,  # filename\n",
    "                     header=None,  # ignore column names\n",
    "                     index_col=0,  # index column (dates)\n",
    "                     parse_dates=True,  # parse these dates\n",
    "                     dayfirst=True,  # format of dates\n",
    "                     skiprows=4,  # ignore these rows\n",
    "                     sep=';',  # data separator\n",
    "                     names=cols)  # use these column names\n",
    "    del es['DEL']\n",
    "except: # read stored data if there is no Internet connection\n",
    "    es = pd.HDFStore('./source/data/SX5E.h5', 'r')['SX5E']\n",
    "es = es[es.index < '2015-12-31']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SX5P</th>\n",
       "      <th>SX5E</th>\n",
       "      <th>SXXP</th>\n",
       "      <th>SXXE</th>\n",
       "      <th>SXXF</th>\n",
       "      <th>SXXA</th>\n",
       "      <th>DK5F</th>\n",
       "      <th>DKXF</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2015-12-23</th>\n",
       "      <td>3109.23</td>\n",
       "      <td>3286.68</td>\n",
       "      <td>366.39</td>\n",
       "      <td>346.14</td>\n",
       "      <td>433.58</td>\n",
       "      <td>375.53</td>\n",
       "      <td>9927.33</td>\n",
       "      <td>614.12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-12-24</th>\n",
       "      <td>3108.11</td>\n",
       "      <td>3284.47</td>\n",
       "      <td>366.28</td>\n",
       "      <td>346.05</td>\n",
       "      <td>433.43</td>\n",
       "      <td>375.39</td>\n",
       "      <td>9931.72</td>\n",
       "      <td>614.38</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-12-28</th>\n",
       "      <td>3093.61</td>\n",
       "      <td>3256.49</td>\n",
       "      <td>364.49</td>\n",
       "      <td>343.54</td>\n",
       "      <td>431.26</td>\n",
       "      <td>374.32</td>\n",
       "      <td>9873.94</td>\n",
       "      <td>611.58</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-12-29</th>\n",
       "      <td>3139.28</td>\n",
       "      <td>3314.28</td>\n",
       "      <td>369.68</td>\n",
       "      <td>349.29</td>\n",
       "      <td>438.43</td>\n",
       "      <td>378.86</td>\n",
       "      <td>10023.66</td>\n",
       "      <td>620.66</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-12-30</th>\n",
       "      <td>3118.07</td>\n",
       "      <td>3287.98</td>\n",
       "      <td>367.70</td>\n",
       "      <td>347.02</td>\n",
       "      <td>435.82</td>\n",
       "      <td>377.20</td>\n",
       "      <td>9956.22</td>\n",
       "      <td>617.48</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               SX5P     SX5E    SXXP    SXXE    SXXF    SXXA      DK5F    DKXF\n",
       "Date                                                                          \n",
       "2015-12-23  3109.23  3286.68  366.39  346.14  433.58  375.53   9927.33  614.12\n",
       "2015-12-24  3108.11  3284.47  366.28  346.05  433.43  375.39   9931.72  614.38\n",
       "2015-12-28  3093.61  3256.49  364.49  343.54  431.26  374.32   9873.94  611.58\n",
       "2015-12-29  3139.28  3314.28  369.68  349.29  438.43  378.86  10023.66  620.66\n",
       "2015-12-30  3118.07  3287.98  367.70  347.02  435.82  377.20   9956.22  617.48"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "es.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import seaborn as sns; sns.set()\n",
    "import matplotlib\n",
    "matplotlib.rcParams['font.family'] = 'serif'\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlwAAAFrCAYAAAAEi1c4AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3XeYU1X6B/Bvksn0DjMMfah36B1BQFCwoq5l7R0L7ura\n0JWVn7q7rorusuqqq2vvvSs2FJCONOlcYIahDjBM75P2+yO5N/cmN20mfb6f5/Hx5tybzJlMSN6c\n85736Gw2G4iIiIgodPSR7gARERFRvGPARURERBRiDLiIiIiIQowBFxEREVGIMeAiIiIiCjEGXERE\nREQhluDPRYIgDARwBYAmAKcA+CuAYgDzAZQA6A/gAVEUyx3X3wsgE0A2gEWiKH7taB8B4DYA+wDk\nA5gjiqI1iL8PERERUdTxOcIlCIIewL9FUfybKIpPArgRQCmAx2APpp4A8CWABY7rxwOYJoriQwDu\nBrBAEIQMx8O9A2CeKIqPA7AAuC7Ivw8RERFR1PFnSnEcAJ0gCH8SBGEugPNEUTwBYCaA1Y5rVgI4\nx3F8rtQuiqIFwE4AUwVB6AsgWRoFc9xnZnB+DSIiIqLo5c+UYm8AEwBcJopivSAIbwuCYAKQB6DO\ncU0tgBzHaFg+gB2K+9c62k4orle2ExEREcU1fwKuWgC7RFGsd9xeAWAagOMAMhznMwFUiaJoFQRB\napdkOq497jh2bffKbLbYEhIMfnSTiIiIKOJ0Wo3+BFxrAXQSBEEniqIN9hEvEfYE+okAPgEwGcBC\nx/ULATwIAIIgGAEUAVgmimKtIAiNgiDki6J4HMAkxX08qqpq9KOLsS0vLwPl5XW+LyQZn7PA8TkL\nHJ+zwPE5Cxyfs8BF83OWl5eh2e4z4BJFsUoQhPsBPCMIQjmAzgD+BiAVwHxBEAQAfQHc67h+rSAI\nSwRBeBT2VYpzRFGsdTzc1QAeEwShFPb8sTfb80sRERERxQK/ykKIovgl7CsRlVoAzPZw/QIP7VsA\n3BRIB4mIiIhiHQufEhEREYUYAy4iIiKiEGPARURERBRiDLiIiIiIQowBFxEREVGIMeAiIiIiCjG/\nykIQERERRasvvvgUxcV7kZOTgyNHDiMnJxc6HfDBB+/i2mtn4aabbsUXX3yKb7/9GtdddyMmTZqC\n2bNvQFJSEgBAr9fj6af/C7PZjP/+9xl89dXnuOqq62Cz2QAAe/aIePxxzYpXfmPARURERO320eK9\nWLfL5459ARlXlI9LT+vv9ZrGxga88sqL+OabRQAAq9WKf//7Sdx771xYLFbs21cMAKitrcHf/vYY\nunbtBgCYMOFk3HDDzarHSkhIwKWXXokff/xedW7lyuXt/l04pUhEREQxy2hMBAB8+OG7qKmphl6v\nx733zgUAzJ59Gw4ePIB//etxdOvWXQ62AKC4eA/ee+8tvPbaS1i9eoXHx//Xvx7HpElT2t1PjnAR\nERFRu116Wn+fo1GhYDQa8dxzL+Htt1/H22+/gd69C3HttbNw0kkTkZiYiNmzb8dDD83FNdfcoLrf\n1Vdfj6KiwbBarbjttpuRmpqOESNGAgCamhrx7LP/hs1mw4ED+4PSTwZcREREFNMKC/vgwQf/DpvN\nhqVLf8a8effhs8++RXp6OpYvX4qLL74UjzzyEJ577iX5PkVFgwHY87dGjBiFTZvWywFXSkoq/vSn\newAgaAEXpxSJiIgoZh09Wob58x8BAOh0OkyZMs2RDG/D+++/jUsvvQKzZ9+O1tZWvPfeWwCAAwdK\n8c03zi2iDx06gG7degCAI1HeJp/r1as3Vq3yPOXoL45wERERUcxKS0tHbW0tnn32KaSlpeHo0TLM\nnn07PvzwPWzcuB6TJ0+FwWCAIAzCK6/8DxaLBWeffR7WrFmJiooTaGioR5cuBTjjjLNgNpvx2Wcf\no6WlFW+99RoAewC2detmnHzy5Hb1UycteYxW5eV10d3BIMjLy0B5eV2kuxFT+JwFjs9Z4PicBY7P\nWeD4nAUump+zvLwMnVY7pxSJiIiIQowBFxEREVGIMeAiIiIiCjEGXEREREQhxoCLiIiIKMQYcBER\nERGFGAMuIiIiohBjwEVEUSXaawMSEbUFAy4iihqL1h/EjU8sQWVtc6S7QkQUVAy4iChqvP/THgDA\nxt3lqKxtxs8bDqGh2YTmVnOEe0ZE1D7cS5GIos57P+3Be47g691FuwEAr809LZJdIiJqF45wEVHM\nKTlSi6OVjZHuBhGR3xhwEVFMOFReLx//4631eOClNRHsDRFRYBhwEVFMeOjVX7FwdSmsXMVIRDGI\nOVxEFDM+/aUEuRnJke4GEVHAOMJFRFHDoNf5vKah2RSGnhARBRcDLiKKGno/Ai5OKBJRLGLARURR\nw58q82aLNQw9ISIKLgZcRBQ1/MmHN5kZcBFR7GHARURRw5+A68Cxet8XERFFGQZcRBQ1/Cn5sHF3\nuXx8rIrFT4koNjDgIqKosG7X8YDvU3y4JgQ9ISIKPgZcRBQVXvhiW8D3kTa7JiKKdgy4iChmmbhi\nkYhiBAMuIopZ+dkpke4CEZFfGHARUcRZrW0rZzp6YF6Qe0JEFBoMuIgo4raWVLTpfmaLDWt2HMXC\n1aVB7Q8RUbAx4CKiiAu0evyMMT0AAK1mC176agc+/aUEdY2toegaEVFQMOAioohLMAT2VpSRlghA\nXXW+srYlqH0iIgqmBH8uEgRhNYAmADoAZlEUTxcEIQfAfAAlAPoDeEAUxXLH9fcCyASQDWCRKIpf\nO9pHALgNwD4A+QDmiKLIZUZEHZzB4HvTaqVsR8DVanK+fTz69nq8dN+pQe0XEVGw+Pu18jtRFE8T\nRfFUURRPd7Q9Bnsw9QSALwEsAABBEMYDmCaK4kMA7gawQBCEDMd93gEwTxTFxwFYAFwXrF+EiGJX\nktHg9XxRr2y8er8zmEpKtF+/YbezWKrZ0rbEeyKicPA34BouCMJ9giA8LAjCOY62mQBWO45XApDa\nz5XaRVG0ANgJYKogCH0BJEujYI77zGzvL0BE8eWuS0ZgcGGOqm3XgWrodM5RMIPefqwc4SIiimZ+\nTSkCmC+K4npBEPQAlgmCUAcgD0Cd43wtgBzH+XwAOxT3rXW0nVBcr2z3KicnFQkJ3r/9xoO8vAzf\nF5EKn7PARetzdrzOnvB+2YyBmD6hEKu2H1OdH9wnF3l5GcjPScHxqib07ZWr+TiZ2ak+R8sCFa3P\nWTTjcxY4PmeBi7XnzK+ASxTF9Y7/WwVBWA7gVADHAWTAHjhlAqhynJfaJZmOa487jl3bvarqAJvT\n5uVloLy8zveFJONzFrhofs4qKxsAAE1NrSgvr8P4ojz8uuOofD4jxYjy8jo8eN1YHK9qQoJNe2Tr\n93O/wWtzTwtav6L5OYtWfM4Cx+cscNH8nHkKBH1OKQp2sxRNAwDsBbAQwERH22THbSjbBUEwAigC\nsEwUxRIAjYIgSKNakxT3IaIOzGaz51/pHdOGowfm4bm7pqB75zQAzrIRaclG9OmaqZpe9PRYRETR\nxJ8RrloA5wiC0BVAFoADoii+JwjCdwDmC4IgAOgL4F4AEEVxrSAISwRBeBT2VYpzRFGsdTzW1QAe\nEwShFPZg782g/jZEFJOkQvPKOCo12SivXrS4JMQnJ3qeNrRYbUgIcNUjEVGo+Qy4RFEsA/B7jfYq\nALM93GeBh/YtAG4KsI9EFKdsNhte+WanHFjp9epASarP5VoY1VvdLo5wEVE0YuFTIoqYqroWrN5+\nFCu2lAGA21Thpaf2R1KiAb+b0sftvnddMlzzMS1t3JeRiCiU/F2lSEQUdAaXES3X1KyBPbPxwj1T\nNe+bm5ms2W5lpQgiikIc4SKiiHEdjNJ7SYZ35Wla0copRSKKQgy4iChiXPOtvK0+dOUpMd4S4EbY\nREThwICLiCLG6jLEpQ9gcaGnEa7v1h5oT5eIiEKCARcRRUxDs1l12xTA6JSngOvHdQcxa/5iHC6v\nb1ffiIiCiQEXEUXM/mPqStGb95zw+76+am09+OqvbeoTEVEoMOAioohxzbcKpKKDcoRr+ugeweoS\nEVFIMOAioohxrZllg/8Rl7KkRG5mUtD6REQUCgy4iChiXJPmA6nooFzROKBndrC6REQUEgy4iChi\nXKcQXQOwQFxzxsB29oaIKHQYcBFRxFhcysKfOb5Xmx/LrBGscV9FIooWDLiIKGJcR7SG9MkN6P75\n2SkAgJz0JDS6lJgAuK8iEUUP7qVIRBGjjIcmDStAeooxoPs/dP04lFc3oVNWsttoGQCUVTSiZ356\ne7tJRNRuHOEioohRjkBdMq1/wPdPTU5A74IMAEBmaqLb+U9/KW5754iIgogBFxFFzJETDc4bAWzr\no2XqyO5uU5KJRoN8bLZY8f3aA6iqa2nfDyIiagMGXEQUMRt3lwftsYwJesy5bCTmXjUaxgT7W5ty\nOnH5ljJ8tGQvnvtsS9B+JkXWofJ6WG02nKhpQnU9A2mKbszhIqLoEKT89oE9s3HLeYPx/OfbkKwY\n4SpzjKYdLm/wdFeKIVuKK/D0x5vl2zod8Or9p0WwR0TecYSLiCKmqFdoCpZK2/5Im2HXNrTipw2H\nAADZGaxKHw/2H61V3WYFEIp2DLiIKCKq6lqw60C1fDuYn5cpSfbB+2OVjQCAl7/ZIZ87XtUUxJ9E\nkcJcPIo1DLiIKCJe+3an6rZy+q+9uuTY63M1tVoAuH84HzpeH7SfRZGx9Lcjbm1WxTDXvrJaPPza\nr9h9sNrtOqJIYMBFRBHRp2umfPzozSchKTF4AZfBMaVocUwpmswW1flNe08E7WdR+JnM7jXXAGD7\nvkoAwLaSCjzy5nocPF6P+e9uxKz5i/H+T3vC2UUiNwy4iCgilNvudO2UFtTHNujtNSakSvbl1c2q\n88cdU40Um9bvOq7Z3uwY0fz3R5vdzi1afzCkfSLyhQEXEUWEFBTdcv7gkD22yWJFU4v7lj9a+y5S\nbLBYraqcPKVAdyogCicGXEQUEVLMk5uRHPTHNhjsAdeO0ir87FidqDqvb2eVVYqY17/d5fGcr7/q\nUY5sUgQx4CKiiJDqYulCEPvoFQ/62bISt/MpiSxBGKtWbTvq1ib9vS1WG0qO1LqdlzzzsftUI1G4\nMOAioojY4KgyrwtBxOXpMeddOwYAYNbY6Jpi13mTCgEAS387jH+8td7jdVWsRk8RxK95RBRRJpPF\n90VBIuX4WCzM4Yp1Y4Q8TBxSAKvVhhM19kURG8Ry6OC5pltGivsG50ThwhEuIoqo6vrWsP0so6Nc\nBEe4Yt/pY3ti9MA8jC3KV+XkeQulLfy7UwQx4CKiiFJuMB1qUn2uNduP4SCLn8a0gT2d20I1NJvc\nzp86urtbm4WrUymCGHARUdgpK793zwtuDS5vEgzOkZCHX/s1bD+XgqNRI7ACgGMa2zVNHtbVra2u\n0YSW1vBNYRMpMYeLiMJuxdYy+TgUSfNaZozpgQQ9v2PGoqc+2oytJRW47LT+mucTE9z/rnqdDgW5\nqW6lIKrqW1CQmxqSfhJ5w3cfIgo7ZZX5cBnSJxdGI9/yYk1VXQu2llQAAD5cvBcAMH10D9U1iRr7\ncOp02qsSzR62BSIKNb77EFH4RSCVJsGgV9Xnotgw5/mVbm09u6jz/rTyAPV6HZIUgZi0ofmaHceC\n3EMi/zDgIqKwazGHPo9m9vlDVLeV+VsUO3IykuRjqayH0WUKcfJw93wti8WGk4cUyLdzM+07Ghyr\nYrV5igwGXEQUdlI9JK3E5mAZPyhfdTvBwLe7WGK12fDfL7apFljUN9mT5hMT1FOIWiOXza1mFPXO\nkW+f5piGHNAj2+1aonBg0jwRhV2Lo9jpxCFdQvYzXJPxkxPd83woeu0+UI31u45rnlOOennSOSsF\n2RmJOGNcT0wcUiDnc1lZGoIihAEXEYVdjePDLzGMQZBRI7Gaotfug9Uez+Vm+g64OmXZpxAvnz4A\nAFBTbC+wa43Agg0igFOKRBQBS387AgAwmcK3YizDkf8ztE9u2H4mtU1lbTO+WLHP43mtMhCjBnT2\n+phSNXoWP6VIYcBFRGGXlmwfXO/aOXxFT6UpxRH9vX8wU2RtLanAK9/sULVdf3aR6nZyovvkTEaq\nc5/Eey4b4XZe2v3HxoCLIoQBFxGFnbQtizGMKwelnC7lli+Pv7NBTsSm6PDUR5ux64B6OrF/9yz5\nePLwrtDr3V83UlNmqhFD+3RyP88RLoowBlxEFHbSh57WB2eo6XU6eXppz6EaLN9yJOx9IG1mi/sU\nc//uWarNqRs8BciOgNpTOCW91pjDRZHid9K8IAjJANYC+EEUxT8LgpADYD6AEgD9ATwgimK549p7\nAWQCyAawSBTFrx3tIwDcBmAfgHwAc0RRZNlfog7G5Kj27VpPKdjSkhPQ0Gx2a1eOcjS1uJ+nyKio\nbVbdTktOwAPXjEF5tXOvxFaTdg23woIMAMCQQu0cPTng4ggXRUgg73b/ALBRcfsx2IOpJwB8CWAB\nAAiCMB7ANFEUHwJwN4AFgiBkOO7zDoB5oig+DsAC4Lp29p+IYlCLyYIEgw6GEO9t6M8I2jer9oe0\nD+S/dTvVZSCuP3sQAKhGuAwe6qlNHtYVd10yAtedVaR5XqrVxREuihS/3u0EQbgawAoApYrmmQBW\nO45XAjjHcXyu1C6KogXATgBTBUHoCyBZGgVz3GdmezpPRLGpur4FqUmhr0ojjWb4U0aAIstiteKz\nZSWqtvQU+2tEGTgbPATRer0Ow/t1QpKHUiNcpUiR5jPgEgRhEIAiURS/cDmVD6DOcVwLIEcQBL1L\nu3Qu30s7EXUgNpsNVbUt6JKbGoafZf//qAF5Hq+ZNrJbyPtBvr3+7S63tqx0e6Cs3BOxrXl/0giX\njUksFCH+fMW8EECzIAj3A5gMwCgIwp0AjgHIgD1wygRQJYqiVRCE4452SSaA447/MjXavcrJSUVC\nQvwXLMzLy/B9EanwOQtcOJ+z/UdrceeCpXji9skQejvzakxmC2wA0lMTQ94fqdh8mpeflZzivR98\nnQWuLc/Zqm1H3dp6dstGtktV+aZWS5sev9kRaCUmJUTl3zQa+xTtYu058xlwiaL4mHTsSJxPE0Xx\nGUEQBAATAXwCeyC20HHZQgAPOq43AigCsEwUxVpBEBoFQcgXRfE4gEmK+3hU1QE2Gs3Ly0B5eZ3v\nC0nG5yxw4X7O5r2wEharDff+Zzlem3ua3N7YbF9lZrPaQt4fafaosanV489qaGjxeI6vs8AF8zlr\nrG+GqblV/fhZyW16/Opq+2dJQ6Pn10Kk8HUWuGh+zjwFgn5nrAqCcBGAKQAmCIJwGYAHAJwuCMI8\nABcAuBcARFFcC2CJIAiPAnga9pWItY6HuRrAY4Ig/J/jZ7/Ztl+HiKJdV8WUocnsXFnWYgrPCkU7\n7XydKcOdm2aXHKnVvIYi4/xJhfKx8jWS7tgpQGujan9wlSJFmt9Zq6IofgbgM5fm2R6uXeChfQuA\nm/zuHRHFrILcVLmApdlig9HxbvPrzmMAgHW7juMPYeqLDuoPaSk3CAAOn2gIUy/ImySjAS0mCy6Y\n0he1jSbNmlwAgDaWbpNSv7hKkSKFhU+JKCSUH2wWqw07SytRfKRGHmkYI3hOZA+1ScMKVLe376uM\nUE/in81mw+6D1Zg1fzG+XlWqec2+slq0KOprXXumgFnnDFJdc/JQ+99sUK+cNvVDKkGiNcLV2GzG\niZomt3aiYGLARURBZ7PZsGxzmXzbYrHinx/8hkff2iBvPDzay8rBYJFqMp3ishKxS456heSCD38L\neV86IqvVhhufWIL579pLOH6+rEQueqt0tMJ3ru6lp/bHozef1OZAXRrhWrPjGKrqWuT2L5aX4Pan\nl+HPL6z2WFSVKBhCXwiHiDqcrSXqEaMPFu+Vj80W+wiDIQz7KI4f1AXjB3UJ+c8hdzabDUs2HXZr\nbzVb3PL3Pl9ur781rshzpSC9Xoeundq+2bmynMSc51fi1NHdcc0ZAr5aWSq3t5gsSDTG/6p4igyO\ncBFR0FW6bNGydscx+bjVkUBv9FAxPFxuOX+wx3Nbiivw3dr9+Nsra1BWwRyvtvhmVSneXbTbrb2l\nVT2KtGzzEZyosb9ePBUtDQbX+l1LNh7G1pIKVZv0ZYBog1iOnaXBTTXgCBcRBZ23qZlGx96GnrZo\nCZcxA/MB7NA89/THm+Xj8spGPHzDuDD1Kn58vnyfZruy0rvNZsMb3zkLniaFsOai1urGpz7arLpt\n8pSoTx2KyWzB859vBQBVSZv24ggXEQWdxctKsIWr7XsXGsMwpeiNp7IU365R7624/5i91s97P+3G\nrPmLIR6oCnnf4plyMcXijeopx+lje4Ts5/pTod6skV9GHU99U2g2tGfARURB88nSYvzz/U0xXevo\nk6XFbm02mw0/rT8EAHjivU3h7lJcUb42XKccO4Vwz0tPezAqSblk1LEp6waWHg1enT4GXEQUFBar\nFd+u2Y+d+6uwo9T3KFBDc2i+RQYiI9Xo13XNLnlHxUdqQtGduKG1ElGijMVd99M0hnlK0dUGsTxk\nP59ix08bDsnHj7y5PmiPy4CLiIJCGWTt3O874Bo5oHMou+OXP108XD622myweZgKffJ99ajWo29t\nCGm/Yt2yzUdUt1/586mYOMS+WrRKsaBicO+21dRqizYWqKcOSBrNBoBg1sllwEVEQeGagAwAPfLS\nPV6fEOGkeQDo3z1LPm41WTQ3UAaA/Uejc8+2aOU6VajX67B6u32l6isLdwKwP6fKshF/DfHCBB0j\nLvLD7oPVIXvsyL/jEVHMOVRej/Jq35W5Jw6NnRpYOujcygR4wy1i/PPfe04BAIweaC9YWttg34z6\nb2+sk6955o7J6NVFe8PfcDhrfK+I/WyKLq98475yed2u4wCA49VN2FfW9pwuBlxEpLJ+13Fs2uM9\nl+WhV3/F/S+ulm83tbjnY3XOSsaeg7GT62S12QIaBWluYVVyV1abDVc//J18e8bYHkhOtFcfGquo\nEL9mh3okMTU5shWKeuSnoUdeOlKSWCmpo5Nqwim98MU2lFc3Ye6Lq/HIm+sxa/7iNi0MYsBFRDKz\nxYr/frENz366NaD7NTSZ3NoKCzLk/e8AYPro0C35b49RjlwybzlcWhqb3X/njm7voRrU1LfKt6eO\n7C4fK8syvPSVehRB2ucwUoSeOUgw6GBhHa4Or6hXtmb7ofJ61W1/RvhdMeAiIpnWSJUvNpsNr327\n0629vsmkGrkYXBi+BOlASKvXrFabXyvZJI1teK7infI5mTikC7p3dm7FE805VJ2ykqHX6zhNTOjq\neM3+5erRqnYpB1HiqY6fNwy4iEjWavL9Dd91FKj4cC12HXBPNN11oFo12qHT63Df5SPb38kg0zlG\nXqw2+8bG/mqMgrIW0eZ/X22Xj11fS56SkeffOjGkffJlZH/7CKdep4OVA1wd3hJHMd7MtERV+3pH\nHpekLcE5Ay4ikrUqCv55ml5Tbs0ya/5iLP3NfYNiifJNyaDXYVBhbhB6GVzSTNexysaA7vfk+5tw\nvCqw+8Q75T6JrtvkeKp5lp+dEtI++XLxtH4A7K8Dq82GFi/bUlF8U/57TvRRE64ttZ0ZcBGRTDkq\n4al4pcVlg19lKYWrTh8oH99z6QgkGp1vWlLOw5O3TsS/b58UlP4Gg5Rb5M+I1WWn9Vfdfkdjc2ay\nc82HGleUH6GeeJfmmPaurGsB0LbcHIoPa3c6R7F8TRkGku8pYcBFRDJp30DAvbq6xOxl3qVLTgoy\nU40Y2DMbQ/t2wuiBzuKm0vRi5+wUZKeHbguXQOlgD7jMGgnTvQrUpQryc1IwSFGssy05b/HqwDF1\nrTKzS2DelpyXYLt4al9cMLmPqi050f6lQHq9v/y19obmFP/qGp0pEIk+Xq9tWaXINbBEJHvju13y\ncUVts1seA+A+wqWUkZqIp++YIt9Wrj6L1iX3UhePK0Y25l41GmkpRowo6oIL7vtanho1GvTonJUs\nX9fSyqQfyfbSStXt4y4jRdFQ6HbmxEIAwL6yWmwuttdcS3KMwtY7VtoePF6veV+Kf78qRriUo/Na\nOKVIRO2SnuLMs1EGX0paI0GStBTPQdXJwwo8noskaWWictPqnIwkdO+cBp1O55aHdvHUfvLt+ibn\nN+KOzGK14uMl9udP2h/xwil9VddkpyehR16a230j4fLpA+TjaF49SeElLaC44/f2Lb+evHUi/nTR\nMM1rbS4RV019C8oqGrw+PgMuIpJ1yXUmMHv6pm/x8tUuLdk9Mbp3QQYSE/TITHUfLYsGyvpQkiQP\n324TEw2q5O/qegZcAFDf5JxaveOykXht7mmYPLyr23Wnj+sZzm55pDW9KX3YpkW4CCtFjpSXVeD4\n0tA5OwVFHvb73OGyX+zdz63EvJfXes3tYsBFRDLlKrOxHpKcvY1wSfkwSg9eNxbPO7Z3iUZatbcS\njc63RuUqumSjwW1EpCPXbqptaIXZYlWt7hrWz/Om5CmJ6mBmikZQFg5a05vXnCkAgCpHjzqWBsfC\nGWXQnaTxngYAq7aVycfK7X68rXJlwEVEAOyr9JSJ8t06pWpe522ES2t6Rq/TRbySuDdaAZdyBERZ\nAFFr5MvsYTVnvCuraMBdz67A2z+IePydjXK7tym6FMUH2XN3TcH1ZxeFtI+eGAxao5r2v/l6sRw2\nmw1lFQ2wsDBXhyIesI9aKfNNXd8f+nXLBAAMdpS4MZmteOTN9fJ5T4uNAAZcRAR7gvPtTy9T7SPm\n6Zuap6T5l+6bFoquhZxWfSjlm2yWYkWlFIgpR8C8jfjFs4277fttLt9S5uNKp8GK0aPUZGPE8qe0\ngmzlqNfWkkrMe3ktPlpc7HYdxSeT2SqPcHlb4CEtJJJWKbrW4vO2epEBFxFhrmIjakmLh6rznspC\nRMMqtLbI0FiJ6SkQkLYq+u89U+W23TG0QXcwffpLiVvbU3+a7PU+0ZKgLo1Udlck8Stfvyu2HAEA\nLFp/UA4sKb69+OU2j+eUX7CkEX4psHrw1V9V13qbAYjNd0giCrmlmw5jS/EJt3ZvZSFikT8hwPN3\nn4L5t064owHwAAAgAElEQVSE0VF9WjlCsutAlae7xTWt2ClLI3iNRnq9Ds/ffQr+esM4VZtkvegM\nsp77LLCN3Cn2mMxWbNrj/l4nefZOZ6kbqaCvp9xNjnARkd+6KTYcfvsH0e28awVxAOiRlx7SPoWU\nS+Dw6M0nuV2SkpTgcQuaaK0vFiprdxzDkRMNaOtagfmzJ+CJCO+fCNj/bq65hcqyKNRx1DZ4X21s\nTDDIrw3XES5X3hbRMOAi6qCsjsRg1zeOPl0zFNe436+20eTWdv9Vo4Lev3BxHajp2sm/WlGXnmrf\n5ifSewGG07GqRvzvq+34v1fWup1LSfJeKFKSn5OKvCh9zrp6WChC8U25h6wnUv6m9H7paerQW+Fc\nBlxEHdTXK0sx7+W1+GHdAVV7stE5YqP1be2rlfvc2gwataxiRVvziqSl4x2pLMQD/1vj8dwZ43qF\nsSehsedQx8zH6+iUaRLD+nbSvEZKI5DeL6TAq2e+enRfWUDZ7THa1UsiilmrHZtOSxXCJRW1zpWK\nrtWUAWCMkOfWlpwYu9NqynBr0lD/q+HLb7wdJOCyWm3w9ptOH9MjbH0h8sZms+HFL7fhP59s8WuT\naWm0Kj3FiFt/N8TrtVKun8XmnFpMS06Q63UpV3q7it13SSJqF09D4ibF8LrWJVV1LQDsuU4lR2rR\np2tmSPoXLmbFL6lVn8kTKf2ng8RbWLvzmNfzWkVviSKh+EitvC/ikk2Hcdpo718GpNIuU0Z09ZiT\nKX2xklazVjgCK6vNBoNeh6vPEPC/r7Z7/Tkc4SLqoDzlLUgr8QDnhr5K9Y4cruz0JEwa1lWVZB+L\nlm46LB8v2+x/TalWR9mMPYeqg96naFRW0ejWNk6xG0GslgXxh6mDFreNVdWOL4UA8M6PuwHYi5rO\neX4llm0+Ip/7decxfPDzHrQ6/r5GL6/h804uBODcHWHPoRocOFaHsopG1DaaPFakV4rffyFE5FWd\nRvI7oL3cH7APnd/331XYXFwBQHs/ulhU42OFkifSG/fKrUeD2Z2opTU1MzGAKdhY8OB1YzXbf9pw\nMMw9ofbQmtb74Oe9qKprwRvf7UJzq73A6YtfbseP6w7iRE0TAO/vadNGdcf/7p2GQYXO4r1/fX2d\nfOwtWJPExzsmEQXM04qsKSO6abbXN5vk/C6DXhc3IxpaZS78IX3j7SgWrt4PADh1dHe5TdrwOV54\nmh53zXOk6FNT3yJvzfPRkr1u5xuanV8wK2pb5NQIAKiqtR/7CpqMCXrNXQoAIMGPdATmcBF1UIUF\nmappolf+fCqOVTWiINf30nhl5eVY19ZVitkZSb4vihPK0S3XVVkXTOmD7PT4ey7mXD4SCz74LdLd\nID/99Y11qKlvxYVT+rid+88nW9AlJ0Ue+frHm+tVpWyaHCNeCX6M2us9rMj2574MuIg6KJNLDpde\nr/Nag6pFsSmrMs8r1l1yaj+8/u0uAIHV1OpISeJ7DzvLJZwyvBsqappximMk9PxJ7h9w8aBzZnKk\nu0ABqKm3pwZ8vty9bM1ve9VV5FtMFhytdH7Z/OFX+5RxVprvLw6eSuBwSpGINFltNtX2Jfk5vgON\nJRudyeWJcZK/BQCZqc7taG44p8jv+ymD0+LD8V2/6fF3NsrHer0OF0/tF7XFS4MmdkvLdQgVNU0o\nq2jweN5XbcDK2ha3tux031tTaY1wDe2bi0Qjk+aJSENlrTqp1PUt5JEbxwMAeig29zUpcp38eXOJ\nFcryGGnJbdva5dG3N6CxWXsRQqxrMfmuwk0Ubtf//UfMe3ktNojlmPeye0Feb5tIjxrQWXNrHn8W\nAmnlcN16/hC/RrwZcBF1QK4LzlzferrnpSM9xaiqw1XUK1s+jpcVioD6jdlTfoY/DpV7/rYdy5Rl\nMzpndZxpNqNBH3eLAuLR859v1SxZ8vD14+TdIFxt2nNCs2BxW79IJiclINGPNIv4edckIr/5U31Z\nr4O8fBpQF0H1J18hVpgVI3eBFD6NR60mCxauLkVNvXO65cPFzhVf500qDH+nwuyOi4fjjHE9kZOR\npPpiYW7jalYKvv1H67yef/IPE9G7IAMLbpvk8ZovNHK92poqodfpkJJkwNA+ufIeq5rXtenRiSim\ntboWcvSwSXVlbQsWri4FoP7A2RtHOUvKfdQMbVyxCPgXxEa7VxfuxKe/lOCN73a5FXQd1rcTJg/r\nGqGehc/IAZ1x+fQB0Ol0qgB8sSKHkSLDarVh1bYy/O2NdV6v65xlzy9MNBpwzRkD/X789qRK6HQ6\n3HPZSJx1kuc9RblKkagDamw2+77I4auVpZg5sTBuv+EXKOqRtWdKMda9++NurNtl3w5lc3EFNhdX\nqD6sbjx3UJtLaMQqZQCurF4eC5pazDCZrchM850IHguaWsy47allPq9Lddmax6AYjZ8wpAvWbPe8\nRVWoUyV8BlyCIOgAfA1gDYAkAP0A3AAgFcB8ACUA+gN4QBTty54EQbgXQCaAbACLRFH82tE+AsBt\nAPYByAcwRxTF+HwXJ4piR1xW9+i8BBpSgVPlSFA86d89Sz42tGOqNNYHuH7eeMit7W3HtiiAejVn\nR6Ec4VKWEYgF//fKWlTVteCV+0/1WKwzlvgTbAHA/Fsnqm4rawZOGdYVxyobsa9Me0oy1Kuv/X30\nVaIo/kMUxQdhD7QuBvAY7MHUEwC+BLAAAARBGA9gmiiKDwG4G8ACQRAyHI/zDoB5oig+DsAC4Lrg\n/SpE5K+3vhcBAOkpRgzsmY1bzx/i8VqDXgebzYYdpZVymzJIiSe+lpJ7o5WEGy/8KYYbjwx650fk\nwePe84aiSVWds5K6sn5erNq4u9z3RbC/TtNT1CuNhZ7OrXgaWyxed8jwdwT3mTsmY7Biix9/+Qy4\nRFG0iaL4GAAIgpAAoDuAXQBmAljtuGwlgHMcx+dK7aIoWgDsBDBVEIS+AJKlUTDHfWYG3GMiarcs\nxzTD6WN7YO5Vo9G7IMPjtfVNJmzcfUJVt+uq0/3Pi4glgQZcJyv2EtRaZh4vLjvNcyJwPGtPAO6v\nusZWnDfnS/y6Uz3VtbWkwmudKW8+XLxHPpaqq+8+WI0KjT0GY8Fzn211a9PKt7rzkuFubcpyDX26\nZgTlb5qRmojcNhTG9Xv8TBCEM2CfWvxGFMWNsE8JSiF/LYAcQRD0Lu3SuXwv7UQUZiMH2Je7jxH8\n+yd44Jj62723AC2WBZrDpXzTj+URLqvNJu8Fd9EpfXHn79UfXB2pqr6S8vXQKSs0hV5f/HK76v8A\ncKyqEU99tBnzXl7bpsf8dedx+fif729Cc6sZ89/diD+/uKp9nY0QZUkayYgB7iU7sjTy1ZIU/0Zz\nM5NRfKRWvn3ljAFt7tPMCb0BBPbl0++keVEUfwTwoyAIbwqC8AcAxwBkwB44ZQKoEkXRKgjCcUe7\nJBPAccd/mRrtXuXkpCIhjrYR8SQvLz4/wEKJz1ngpOds5wH7CrRePbKRk+H7m1qaYsuLS2cMjNvn\nvqBLptuUg7ffNUUxfZGRkRKTz0vxoWrc9dQvAICJw7riht8Nw+HyetU12dmpAf1usfg8aLn6nMH4\ncZ1925fzT+kXkt9r5/4q+VhnTEDn7BTMmr9Ybgv0Z7oW/KxvMuGP/7bnP9lssfm3yclKAVCN1/7v\nDMz6x48A7KNMkjsvG4n6JjN6dtee5rv/2rHonG3/92lSrNDunOss7PzMPdMCfo1/veB3Af0e/iTN\nDwLQRxTFbx1N+wD0AbAQwEQAnwCY7LgNx/8fdNzXCKAIwDJRFGsFQWgUBCFfFMXjACYp7uNRVVVs\nJSq2RV5eBsrLYyc/IBrwOQuc8jk77kgAbm5oQbkfFdJbWpzX9O2SHrfPfWVFvSqPw9frrLnJ+bxU\nVTdG5HnZtq8Cr3y9A4/dMhGpHgo9eiMFWwCwemsZysvrUOcy9dQpzej37xZv/zavOVPA2z+IqK1r\nCsrvVd9kwsHj9RjU2z04WLHxICa5lN44drw2oKR313IermLxb7PvcA0Meh3MLa1y2+L1B+Xjwrw0\nZKUnefzdhG72sZ7y8joMLszBjlJ7kDu4ZxbGDMzDjLE9kJGoD9pz4ylw8+dfZwuAWYIgjASQCHsA\ndQcAE4D5giAIAPoCuBcARFFcKwjCEkEQHoV9leIcURSlMbyrATwmCEIp7NOZb7b1FyKi9vOWQKqk\nXGrdp2umlytjW8BlDxSXR6IOV0urBf/+cDMAYNH6g/jd5MA2kt6lGF0BgIE97IshEhSrtQb0yPL7\ndRKPpFlFW5DW09/xzHIAwLVnCfIG4JLkxAQcc1kNKe6vwqDCXL8ff4PoPcG8+HAN+sXQopclmw7j\naGUjstIT3V6Hf7hgKHburwqo9IUUbAH2lIDbLhoWtL764jPgEkWxBMDvPZye7eE+Czy0bwFwk9+9\nI6KgW7/L50w+AGDuVaMx/137psXKYfiEDl6NXSlfsYFzJHLm3//ZmRydn50Cm83mV9Botdpw21PL\n3PZJvGHmIADqXBjXoKCjkUaXgp2j99b3orxaWJKWnIC/vKTeF3CdWB5QwCVNgXry7qLdeOj6cf53\nNIJaTBa8/YP9Oaqpb1WdO318L4wryse4osBSwXW6yJVw6bhfW4g6qN/2nvDruoxUZ37SR0uc27t0\ntOKX3kwf00M+DvcqxS3FFVi2+Yh8++VvduDGJ5b4tbJt3a7jbsHWfZePRJccZ/mH5+8+BbddOEy1\nErMjkhLngxFwfbx0r9fzWhsu+7Ng4XB5PRpcUgMmD+uqWc6jpqHVrS1a1Wr09f4rR2Fo31zcfEHb\nRqYGO6ZyPe2zGEoMuIg6GJPrtj4eJGksu76iHat64lGCQY9zHKuVio/UQDxQhUY/cuLay2az4emP\nN2ue82dlmzKABoBbzh/sNoqSkpSAMUJehw+wpV+/vfFWZW0zvltzwOs1Wv82u+R4Xh1ptdnw5xdW\n4cFXf8Wfnl6OzXtPyNNu500qRPe8NLf7VNW1YF9ZLdbsOBrgbxB+yoBLKkoq9MrBPZeOREpS2wIm\n6fWcnxP+2nLc2oeog/H3m7pWnZlQb30RKV1yUlBR27atW6RCi/vKavHTenu19tfmnha0vmk5cqJt\n9ZkkVYptagpyUzFhcMcexfJGnlJs5wim64iiltKjzpIFZ53UC9+vPeB1f7/quha5zhYAPPPJFvnY\nmKCHp1D5kTfXAwD6dctCXnZoyl2018bd5fh6ZSkAYIyQhz9eMDQojztqYB627avE2KK8oDxeIBhw\nEXUwPfLSsUEsx7RR3X1e2697JooPOz8EjHGaPP3oLRPanPTeKcsemCqfp1Crb/I9ilZ8pAbLNx/B\n1WcI8qiHzWbDWkWBzQW3TUJORpKnhyA4pxTbuyiiscXz/qUzJ/XBwpX75EC6X/dMeTrQNdAzW6zQ\n6exV8Nd7SZBPMOhh9rEdV01Da1QEXK0mCxZ8+BvOn9wHQxwjrcpip/26ZQVtpHXayG4Y1DvH68hh\nqMTnuycReSRtQj1xSBef15adUK+Y6tbZfYoiHuh1OtU2LoGwWMO/HexqLxvwAsCxykY8+tYGLNtc\nhi3FFXL7iq1leOmrHQDsU2UMtnzTyUnz7Xuc7SWVHs9Jo85SADWyf2eUHrWXKHjrB2difWOzCbf8\ncylufnIpAKCmwfOorNGgl/+tJxkNuPYswe2aJi9BYDg9/s5G7DlUgwUf/AbAPv2q1LNLetB+lk6n\nQ0FuakSmyhlwEXUwa3fYP6y1crRcuX4rj+eSEG3V1kCtPZTJ8lp5OsqVbsqPlXWKCuQxXBg/rKSy\nEO2ZUqypb8EXK/Z5PG8yqYP2xAQDtpXYA2VlXte2fc6gbdb8xV5zwgwGnRxw9eqSjmkj3Ue0G5uj\nI+Da77KTxevf7lTdTgjDFkvhwICLqIORcj6yOboRFJH8KDh/UiGuP7vI6zWfLisBAHy3Zr/qA5v8\nI+VwtWdK8WlFbpWr3l0ycOG0fqq2pEQDhJ7O7WxsNhtMZivqGv1fkGHQ6+QpRU911MSD3oukhoPW\nCPGuA+p+5bRh38JoxICLqIPKTPW/WCBg/2CgyFMuejh/Uh/VZrwpSe6jllJe0MdLi0PfuTgkTT0t\nXLMf20vbFrAO66tdR+uO3w/Hg9ePdZveMibocdFUZxD2ydJizP7XUry7aLffP1NryuyeS0eobi91\nFBUNp/omkyp43XOwxu2arp3Uo7Z5WQy4iCjGHHLZIy8Q4wdxr3kt4U4FqXasMBwr5EGv16GT4tv/\n9DE9Ne9jMruvkEtt47L6jkaaMa5rNMk5RoHKSdceTTabrdDrdG4rhxMMetU2Td+t9V5OomsnZ4mD\nk4cWYIBjxwBnSQv74w/p4x74uW5MH0qLNx7CHc8sx9LfjuDRt9bj3UW7sXq7ujxFeXWT2/tUvJQm\nYcBF1IH89/Ntbb6vIU5XKLaf+4fBrzu9J7W3x4tfbgfgXMCg3MTXUxB164Jf3Nom+LFoghDQPoae\ntChytF7586nycaLR/m+qc5Z6xZxepwvo5545vpd8fNO5g/GXq8cAcH9lagUu4crjqm8y4Z0f7SN0\nb/8govhILX7ecEj1hQGAapFHvOE7KFEcsFiteG/RblUdHy3tmT7glj7alBX5JVJQFGyNzWbsPWyf\ngumvsR+epyrzrulH/3ftWFw5Y2DQ+xePdC4J24FWnK+ub1EVmtXrdchKtwfJORn2YCMtxagq5KnX\nQzVV7MtQjZErALh4Wj8kGQ246BTn9OSfLlZXaNeqbh8KD7hsWSRxXUygnDbtkpOC8ycVhrJbYcWA\niygOrNl+DD9tOIS/v7Her+vvu2JUwD+jI29g7I00feNJY7NJXi3WXu/86CwRoJweuuHsIvTrnqna\nlHjikAIMLsxxe4zX5p6Gvt0y5fpS5J3rqz7Q5HmtzaQfvn4c7vz9cPTMd5Y7UJZoSDDo/ZqqzstO\nxmmju3vc/mdAj2y8MGcq+iteo6MG5OGRG8fLty1Bem36oqwd508wed7JhXh89kRcMKVvKLsVVpzE\nJ4oDry7c6fsiBV9BgpZAvnF3JN7yS6w2G25/ejmA9lefX7P9KNbscE5VKn/ulBHdMGVEN7SaLHjj\nu10AgBvOKcLeQzXYUVrVrp/b0bkGpoEuVlSO2Dzs2DQ6Oz0J2f09rxIe1DvHr7ylh68fj9TkhIAD\n+q6Kenqtfm711R6u9b60RtWMCXpVCYziI+7J9LGOX1mJ4ozZYsWrC3dg1373D9qkRAN6d8nwe7Rq\neL9O8jFHuAK3r6zt1efrm0y457kV2O4o5fDS1zvkc1rTiQCQaDRgeL9OyEw1IsGgd9sW5u+KkQ3y\nj2vg0576ZVqrSF3NuWyk3//WpGn+QP9tKvPD/N1btT38mWJfcNsk1e0/BGkrn2jCd1CiOHO4vAEr\ntx7Fk+9vktusNhu+X12KllaLnKjrj1kzB8nHzOEKjM1mw8uKIClQXywvQXV9KxZ8+JvbVj53XjLc\n4/3uumQEnr5jCgCgu8vOAD3yglexu6NwTV6vrm/bnpuAf8WG87L9L4GgDLT+dPEwzLtmTMB9MgUw\nOmYyW9tUj2xrie9EeGlPUklasntuZKxjwEUU4xqa1R/GWpvkbhTL8fwnmwEAiQFsQK38sOEqxcBs\nLanE8aom+XagH1SHyp0J8OIB9Wilvx9GSYkGbt/TTjqXl/3yLUe0L/SDMcFzwPX4LRNw6++GID8n\n1eM1ADBjbA/5WDndOWpAniqHzxdphwJ/R7haTRbMeX6lz5XOza1m1etVOd15wznei/TGO76DEsW4\n711q9CirR0tvpuU1zg/+7QHk9CgDLo5wBebwCXUtoUBXg+1W/B1/XHewzf3o143bMbWH6whXWrIR\nVXUtWLi61GewolzROLRvrtcpxS65qRg/yHepjpMGB6ecx20X2lcr+htw1TS0or7JhA27PW+YDdiL\ntD7x3ia8/YOIfWW1WKPY93PK8G5t73AcYMBFFOMaXOrofO7YygUAtu2zD+W3Ne9EuU1gQgT2DIxl\nrnvvBZLYXHxYnTC855DzdqAjVtecad+0+Mzx2kVRyTvXfzs6nQ7Pf74Vn/5SgsUbD3m9b0urc7T5\nnktHBqWAZ5ecVJwxrifuumSE74u9kL5A+Rtw1Ta2+nXd4o2HAQBLNh3GI2+ux2uOfRGlfNBn7pgs\nX6vMEe0IuEqRKMYt3XTY47n1u45j1IC8Nu8Dp55S5AhXID79pUR1u9VsRZLR5vVD12azn69r0t4z\nLycjCfdePjKgfmSkJrZ7hSQ56QCUltmrs9c2aAchB47Voa7JJG+HlZYcvI/aBIMOl08f0O7HkaY3\n/fkisHrbUbz8jTMfUXqdBuLckwsB2F+Pd/5+OFpMFnTPS8eW4gp0dtm6x9f+oLGKARdRHFu9/Rj6\ndstSffjPCeADW5kjEi/ba0TKXf9ZAcBzeYhd+6vw5PubMH1MD48jJ1fOGOC2zxyFlg3qLytZ6Yny\nVGGWhy17/vr6OgDOf2uDCrULk7ZFsFYLGx2P48+0qDLYAgDxQDWKervXePOmm+J1O6J/Z/n4jouH\nq+qEAUB+trryfrzgHAFRnHPd8Fbome33fVUjXKzDFRQnFPl0StKq0p83HJKnsQa5fKgZA1jwQKFx\nTLEQwte/CWnvxWCOcAXr36H0WvK1SlGrcKunHQ1cp9EluZlJqr0hlUYO6CyvUJRWULuWM4kX/NdL\nFMOUU4VFvdwDqRSNvfUC+YasHNQKxp5ypE6G96V3QYbqtpErRSNOmSOptc3PztJKt7ZMxX6XgVDu\njXn+pEKcP6kwaCPNWjlcdY2tWLPjqOp9pVVj1fPbP+52awOAuf9brdleWetfKY1Hb5qAm88djL5x\nutCDU4pEMUzKvxjaJxdXzBiAeS+vVZ0f3DvH56oib5Rv7twKxj+9CzKw/2idx/OBfPgqt34BgD5x\n+kEU1bykP7pWUAeAfzpGtZS09tv0x9N3TMai9QeRkZKIycO7tukxPNE5NshWjko9/9lW7D5UA71O\nJ6+Y3HXAv1XNNpsNJ2qa29WnTlnJmJhV0K7HiGYMuIhiWH2T/Q1fr9dpFlV0DbZOH9v2lWoMuPyT\n4ON5ajH5v1pRWbj05T9Pg4ErRcPO23IT16R5rQAM0B5p9keCQY+zT+rdpvv6w2DQqcqVSKthD5XX\nywHXyq1H/Xqswye0pxnJif96iWLYh4v3AAC2FFf4lfdw2fT+bf5ZjLc865RpX2V1y3mDfQamJrP7\nFI0nygR5BlvRx7XIsLJ8h1K05t7p9eoRLqNRnUhfowgou3ZyFmQdNcCZ9C55zyVX9PLpA3DtWUJQ\n+xvrOMJFFMOUU1fKCvLZ6Ymorld/++7aKa1NeViFBRkoPVqHrDRWLPfk0ZtPQkOzGTkZSVi2WV2J\n/LyTC/H1qlL5ttZmwVpL8+dcPjJqP6g7km5eVoW6rvA74mGUJ1r/jgadDhar83cwGvRoNVnl36tR\nsYvF5OFdMXlYV9z5nxWa7yNVivebBIMOZ4zrCZPZgu37KjF9dA+36zui6HwVEJFfyqvtORMZqUYk\nGg2YMbYHMlKNeMBlT7WR/TvjxbnT2/QzHrhmDJ6+Y7LHVUZkX1UlFSR1XUVW2FWd+O46KvLuot24\n5Z9LVW3zrhmDIUEsJUBtl5qcgOljtAMG14DLU1HaqA24XKYUpdem9Hspc0KnDO8m/x5aXxqUK2ql\nKvbGBANuu3BYwCUk4hXfQYlilNlilVdJPXz9OADAlTMG4soZA92uvXhq3zbnYCUY9G1eZdURuW6d\nNLBnNjLTEuV8H+WqrxM1Tfh5g3vNrYw05/P9yI3jmT8XYZ5Ghl0Dj0YPOVzRurpUr9fBYrG/h/y2\n5wTMjuPV249ixdYy+bpzJvRGeopRXr24taQCh080qHIMq+vsKxGfu2sKUuNw4+lgiM5XARH5VNfo\nHO7PzUz2ciXQPS/d63kKjRljeiAt2Yg//G6I3KYcFflkabHbfcYW5asqb3fPS2ex0yi1fV8lHnp1\nLcwWK2w2Gz77xf3vCdg3EY9GiQl6eVTrvZ+cOVhmi021pZH0mlWuWn7wFfWK6N/2nrA/ZpzW0AoG\nBlxEMaq51f5tul93lgqIVltK7HtZCr1y8OB1YwEArYpVir/uPK66/pJT++GPFwxlzbMYcqi8AY0t\nZuw+WC3va3rGuJ54fPYE+RqtFcTRoLy6GTUNrVi1rczjdlKA9229TGYLvl97QL7N165nDLiIYpT0\nYV18uDbCPSFPBityV6RFDS2OVYpay+hT21g+gEIr2ccIlcViU+Xm9euehS45zlV9yYnR/Xd95Zud\nOGlQvsfzUzzUALPZbPhqZSk+WrJXbmO85Vl0vwqISFOLyYIvV+wDAIz38kZJkTVtVHf5WJpq2X2w\nGr/8dlgzz6Wt9ZootApyU72eN1usqpEds0tuV5Ix+sc2lm0u83hOo6A+AKC8ptmt2Cn3XPUs+l8F\nROTmDwt+kY+njujm9dpA9k6k4FKuWJRGuA6XN+DN70U0aEzhcCVodDppcBdcPLWvx/NmixWLNx6W\nb0srU6XttqI1h8tf+TnOzaTPGt9LPn720y0+C/2SEwMuohiX4yNh/r4rRoWpJ+RKubrQNZn4rR9E\nt+s5whWd9HodzpngueK7xWJTLXSQFjnce/kovHRfbO8QkJ2eqNp/9aTBXeTjw+UNMETpCsxoxGeK\nKMZ5qv0jYUmByFFOr/hTiykvO8XnNRQZyr/l32aNV507UdusWZtKr9cFtFl8NLrnspGq2906q6dX\nlQn1rjXoSC22XwlEHZDrfm2eVkC9OGcqXrhnaji6RB4oP3+8ffBeMX0Azj25kPXOYoTrpuIrtpTJ\nOwzcf2Vsjyhfeqp6+69OLiPoxgQDnrx1onx7iWIq1eop2YsAMGmeKOZUKJJUn7/7FI/XsR5OZCQa\n9XLpB38+fq49U1Al11PsKeqVjY2OjeLTYrzopzKPMDs9UTP/rLOHkVjGW95xhIsoBlitNsx/dyMW\nru2JIYIAACAASURBVC5Fdb29ovOFU/ow5ycKKXPmXFeraYnWbV/If8pitrGeIK8sTTJ/9kTW1Qoi\nvlsTxYDdB6vl/2Y49nVL5/RTVOrXLUs+9ucbf6zn+HQkQ/vkagZUSzY5p9V85VRGO+WXuEBHydNT\nYnt0L9T4L50oBhQfqZGPf3LsvccE1eh11yUjcMqIbuiep96SZ+KQLm7XcgAhdtxz2Uh5Y+Y/XTRM\nblfWooqlAPrvLsn/QNtXyk4e3hXzrh3T3i7Ftdh5ZRB1UC0mCz79pcSt3WplwkS0Gt6vE64/u8it\nCOTl0we4XWvh3zEmjRqYhweuju0Ao0d+Os49WV3uIiXJv1Et5eKACYO74Iazi1TV9ckdAy6iKLdR\nLNdsnzRMe7sNil4ZqYk4fWxPVZvFwoArVnnbYzBWuOZo+bvvY4FiQ/Vbzh/CCvN+YA4XUZTbdaBK\ns53J1rHJtQYml9LHrniY1u/XPUt1OycjCVNHdsMgxT6gWowxNHUaLXwGXIIg9AXwDwAbAPQEUCGK\n4iOCIOQAmA+gBEB/AA+Iov2ruCAI9wLIBJANYJEoil872kcAuA3APgD5AOaIouh7GQ9RB7Z8i/se\nZ4MLvb8ZUvTqXZChum2x8C0wVsVSvpYnysCqU2YSdDodrjuryOf9UpIMmDikAAN6Zvm8luz8ebXk\nAnhfFMUFoijeBeByQRBGAXgM9mDqCQBfAlgAAIIgjAcwTRTFhwDcDWCBIAjSO8w7AOaJovg4AAuA\n64L76xDFnx559iKLr95/qtz2xwuGebqcotz4QerE+ZwM71szUfRKiIMpReUoXVKi/5NeOp0ON583\nGNNGsoacv3wGXKIorpdGqBx0ABoAzASw2tG2EsA5juNzpXZRFC0AdgKY6hgpS5ZGwRz3mdnu34Ao\njtU3mXCovB7JiQbodDqcOb4nhvfrxE2OY5gyZ2b8oHyM6N8pgr2h9oiHEa5At5+itgvoXVsQhAsA\n/CCK4m5BEPIB1DlO1QLIEQRBD/tU4Q7F3WodbScU1yvbvcrJSUVCQmwXkvNHXl6G74tIpSM8Zw/O\n/wkA0NxqQV5eBm6/bHS7Hq8jPGfBFsrn7JzJfZGfnxmyx4+UjvI6y8hSV1yfd8P4Nv/u0fCc9e+Z\nHRX98Fcs9RUIIOASBGEa7FOFdzmajgHIgD1wygRQJYqiVRCE4452SSaA447/MjXavaqqavS3izEr\nLy8D5eV1vi8kWUd5zg6XN8jH7f19O8pzFkyhfs6qq5vi7m/SUV9nhQUZ6NclvU2/e6SfsxtnDsKq\nbUdx4aQ+MfO3i/Rz5o2nQNCv8UNBEGYCOFMUxbsEQegqCMIEAAsBSDtYTnbchrJdEAQjgCIAy0RR\nLAHQ6BgZA4BJivsQkRfnTyqMdBcoBJpbzb4vopgQy2URJg3rivuuGMVUhRDzZ5XiaAAfAFgnCMIS\nAKkAngfwAIAnBEEQAPQFcC8AiKK4VhCEJYIgPAr7KsU5oijWOh7uagCPCYJQCnuw92Zwfx2i+JKS\nZEBTiwUXTOkb6a5QCDS1MOCKF/vKan1fRB2az4BLFMWNUE8RKs32cJ8FHtq3ALjJ794RdWDNrWY0\ntVgwpE9upLtCIcIq80QdB5ckEEWpE9X2/dnyslN8XEmxijVPiToOBlxEUepIhT1hPjPVGOGeEBFR\nezHgIopCjc1mvPjldgBAWjIDrnhl4xAXUYfBgIsoypRVNOD2p5fJtzmlGH/uuHg4euSlYcKQgkh3\nhdppxpgeAICUJK7wI+/4CiGKMiu2qvdOLOwaW8X9yLeRAzpj5IDOke4GBYHesTUOp/7JFwZcRFHm\nuzUH5OMLp/RBdnpSBHtDRN6cfVIv7CurxcyJhZHuCkU5BlxEUcS1LtPRyvjfaYEolmWlJ+EvV4+J\ndDcoBjCHiyhKWKxWfLasRNV28dR+EeoNEREFE0e4iKLEnOdXobahFQAweXhXnDGuJ3IzkyPcKyIi\nCgaOcBFFgWNVjXKwBQDTRnZHj7z0CPaIiIiCiSNcRGHy7o+78fPGQxjZvzNuPm+wahn5ko2HVdcW\n5KaGu3tERBRCHOEiCoNZ8xfj542HAAC/7T2B255aJm92a7ZY8eO6gwCAQb1zMHVkN6Qm87sQEVE8\nYcBFFGLLtxzRbH/kzfUwma14/+c9ctt9V4zCdWcVhatrREQUJvwaTRRir3+7Sz4e2icX2/ZVyrdn\n/2upfJyewsKJRETxigEXUZBV1bXg9e92IjkxAZt2l8vtf79xPLp1SoNer8NDr67FofIG1f3+cfNJ\n4e4qERGFCQMuoiB7+evt2HWgWtV21ekDVasOXYMtAMhMTQx534iIKDIYcBEFkc1mcwu2AOC00d09\n3mdo31xM5CbGRERxjUnzREG0+6B7sDV+UD50Op2q7Y6Lh8vH91w6kgEXEVGc4wgXURA98d4mAEBR\nr2x065yGol45GDmgs9t1Iwd0xt9mjUfnLFaSJyLqCBhwEQXJ3sM18nFlbQv+fOVor9f3zGcleSKi\njoJTikRB8tjbG+Tjv1ztPdgiIqKOhQEXxSyzxYqWVkvYf+6W4gp8sbwEtz21DI3NZgDA0cpG+fx9\nV4xCVnpS2PtFRETRi1OKFJNKDtfgzn8vBQC8dN80JBic3x2OVjaiU2YyjAnB/T5htlhxyz+Xqto+\nWLwH159VhAdeWiO3FRZkBPXnEhFR7GPARTFnwQebsL20Sr59/4ur8c8/noy/v7EOB47VAwDOO7kQ\nF57SN2g/02q1uQVbALBiSxl6dE6Tbz98/TjVptREREQApxQpBimDLcBe2f2mJ5bIwRYAfL2qVD4u\nr25Ci6ltU4/1TSaYzBYcOeFeqFTyweK9AIBzT+6N3hzdIiIiDfwqTjFl0fqDfl2XkWrfl7CqrgX3\nv7habn9hzlQkGQ1+PcaBY3X46+vr3Nr/d+9UGBMMmDV/sap95oRCvx6XiIg6Ho5wUUz4bFkJXvxy\nG97/aY/c1rVTqua1XXJTUddowterSvHpL8Wqc+KBKs37aHnlm51ubXf+fjiMCfaA7Z9/OFluT0ky\nICnRv0COiIg6HgZcFPWaWsz4ZlUpft15XG47c0JvPHrzBMyc2Ft17bxrxuCYY8Xg58tKsGrbUdX5\npz/eAgCobWhFyZFaAPYpR5vNhre+34WfHCNoFqsVh8rr4apAEeR1ykpGZpp9/8PLTxvQ3l+TiIji\nGKcUKWrVN5kAAHc8s9zt3K0XDUdVZQPGCHlYuHo/Jg7pAqFXDvp2y8SVMwbgPcVImCvXqUAAEHpm\nQ3RsyzNhSAF+3nBIPnfuyYUYK+ShrtGELjnqUbWnbp+EqroW5GayYjwREXnGgIuiks1mw93PrkBa\nitHtXEaqUS4DUViQiWfumIy0FCP0jv0Kp4/pgY27y+VNpEcPzMPYojy89NUOjz9PVOyBqAzwBhfm\n4CIvqx11Oh2DLSIi8olTihSVPlqyFxarDbUNrW7npo7sprqdkZooB1uAPQjae7hWvr19XyUmDC7A\nzecODrgf159dFPB9iIiIXDHgoqj0w6/q1YhD+uTiv/ecgtsvGobfTe7j8/5mi1U+vv2iYQCAiUML\nVNekO0bPxg/K13yMuVeNRueslID6TUREpIVTihR1GptNbm3nTuyN5MQEjB6Y59dj3H/lKDzx3iYM\n7JmNIX1y5fbBhTnYUVqFScMKcONM54jXDWdboNfr8MnSYixafxDTRnXHwJ7Z7f9liIiIwICLotCb\n34vy8agBnZGcaIDQKyegxxB65eC1uae5td/5++FobrUgIzVR1S6VdLhixgBcMYMrDomIKLgYcFHU\nkdKxbjlvMCYMKfB+cYCMCQa5jhYREVG4MIeLosr20kq53lZR78BGtYiIiKIVAy6KKs99tlU+zk5P\nimBPiIiIgocBF0XEqm1l2FdWi/omE1odG0uv3FqGllb78QPXjIlk94iIiIKKOVxRyGyx4s7/2Itv\n/uGCocjLToHJbMWnS4uRkpyAW84bEuEets93a/fj4yXqPQ6f+tNkvLrQuXdh/+5Z4e4WERFRyDDg\nijCT2YLz5nyJgtxUjBHycNroHpjz/Er5/L8/3Ox2n0G9cjBlRDe39nAyW6z4ZGkxTh3d3W27G2+s\nNptbsAUAdz+7Qj5++PpxQekjERFRtOCUYoS9u2g3AOBoZSMWrt6vCrY8+WLFvlB3y82yzUfw2Nsb\nYLXaUN9kwi3/XIof1x3EX/63RlVk1Jebnlji9fx9l49E74KM9naXiIgoqnCEK8KsNu32pESDnM/k\n2jY4zKv3WloteOO7XQCAm550D5gefXtDwKNSZ4zricunD4DNZsMPvx7Emh1HMWNMTwwqzPV9ZyIi\nohjjM+ASBKELgH8AGCGK4nhHWw6A+QBKAPQH8IAoiuWOc/cCyASQDWCRKIpfO9pHALgNwD4A+QDm\niKLo/9BIjHvnRxGLNx4GAJw+tieumDEAG3eXY8WWMs3rX7hnKo6caEB2eiJMZiu2lFRgRP/OuOs/\nK9DYYm5zPx58dS3Kq5rwwpyp0Cn2H/Rk1vzFHs9NGlqAlduOYv/ROsyav1iz0KjSsapGAEDnrGRc\nPt1eXFSn0+Gsk3rhrJN6BfBbEBERxRZ/phQnAfjSpe0x2IOpJxznFgCAIAjjAUwTRfEhAHcDWCAI\ngjQ/9A6AeaIoPg7AAuC6IPQ/JpyobpKDLQBYtP4gTGarqgSClm6d05CabERWehKmDO8m7/13pKIx\n4D7YbDZsKa7A4fIGtJqteOpj99wwiclsH1k7XF7v8ZoX7pmKG88djN5dnNN/ew/VwGS24tlPt2Bb\nSYXq+lnzF+Mv/1sDADhR0xxw/4mIiGKZzxEuURQ/EwRhqkvzTNhHvQBgJYA3HMfnAljtuJ9FEISd\nAKYKgrADQLI0Cua4z1UAXm9f96NfZW0z/vziarf2ilpn0HH7JSPQs1Mqfvj1ABZvPIybzxvsdj0A\n6B0jUscqG2GxWmHQ+5eCt6O0Ev/64DdV27aSSrz/0x4sWu/cJPqSaf1wtLIRy7eUYe5Vo/H92gPy\nue55aXjkxpNgsVphMlvlrXAeun4sbnTkZdU2tmLD7uPYtOcENu05gVfvPxVPf7zl/9u78/io6nOP\n458sEPalGKSAuAEPmy1eKgoICFhc6FWv1utyq7VKtSoVrkqxel3qVhW3opVrqxbt4lJq21evVStU\ntJVaixUBlwcQrYIKQdkUWZP7x+9kmISE5MScmWTm+369eJlz5szkyeOcM8/8tsPiasXXGeP71itu\nERGRXNHQMVxdgU3RzxuBzmZWGO1/Pe24jdG+tWnHp+/PaRUVFVx6z/zU9tTTDuZHv36VbTvKufwn\nobVn+KBuHHXYfpSVbeIb440TRx1Im1Z1/2+ZPe8tThm753v+rSz7hNnz3mLRWx/V+Hh6sQXw63m7\nZg/e9Mt/pn4+65h+jIpmRRYVFlLUclehV1BQwDkT+nP/E29w9+OLq9zw+aoHXmJV2adVfke/Xp0Y\n82896/jrREREcktDC67VQHtC4dQBWOfu5Wa2JtpfqQOwJvrXoYb9dercuQ3F9bj33c7yCtZt3MJe\nnVrX7y/IgBmPvpL6eea0sfTs2p5ZT71J2brPUvtHDO4BQGlp/WbmHdC9Iyve38DbH27a43N2llfU\nOP7q9imjuGLmfD6LMQ7s+DF9KC6qvTVtQO8dQFhDa+l761P7qxdbJ4/rw5nH1tx61xD1zZnsopzF\np5zFp5zFp5zF19xyFqfgSh9h/QQwDJgNHB5tV+6/EsDMWgD9gOfdfaOZbTazru6+hjAu7AnqYd26\nuscrbd2+k/Nvey61fdVZX+GDtZs5bODe9RoYnoQZsxexcPlaILRilRRAWdkmOrdtWaXg6tcj1KFl\nZZtqfJ3qjjm0Fz/+7WKWvrue82+aw7XnHFrjcTentVABXPOtQ+gVjbe6e8pIFi5bS4+u7bgs6u68\nf9oYXnxtNYP77MWv5izlhcUfAnD84fuz7uOqhVN17VsW1jirstIlpwzm6X+8y8hB3er9d9altLR9\no71WvlDO4lPO4lPO4lPO4mvKOautEKzPLMVRwBlANzO7nDBA/grgJjMz4ADgUgB3/7uZPWtmNxBm\nKV7i7hujl/oGcKOZvUMYrP/g5/mD0l3/0IIq29fOCtsd2rVkYBaWGXj7g42pYgvgnAn9Uz+fd/yg\n1FpbwxpQEHbpuOv+givLPmXT5m3sLK/Y7b6DntbSdMb4vqliC0I34MF9S6u0chUUFDBsUDcAzj62\nPxUVYUzWhGH71hlTcVEhd0wawQW3P7/bY9PPH06Xjq0YuL+WexARkfxVn0HzzwPVP0m3AufVcvxt\ntexfBEyMG2B5RUVqsHh1FRUVqQHbNVmxakNGC64Fb67hX6s3seTtjwEYuF9nLj5lcJWiqnP7Eu6f\nNoY3/rWOPj071fZStWrTqkWV7ckzwgrtt104gusfWsCkEw9i/y/u6r2dMXlkanZjda1Lijl5zIFV\nijEIxdfEr8Xr+mvVspippw5m+iML6dq5NWuiVrwuHVvFeh0REZFc1OQXPp1487P8ZOoRFBcVsnnL\nDibdGWq/wb334qTRB6SOa9e6BTMmj+SRucv40z/CYPAV72+s8TUbw9yXV/LLZ5YybkhPTh3Xm7kv\nr+KRuctSjxcA/12t2Eo9VlDAgAYWgq1b1jyerbLV7LoHF3D3lFGp/bUVW5WOObTuFqz66r/fF3jg\nsrFs3b6Th+cs5ZjDGu+1RUREmrNmcWufc6fPA+CGn+/qOly4fC1X3v9SavuGb4exTKeO68MDl42l\ndUkRH23cmkg8ry5fm7olz9yXV/LtW+ZVKbYAJp10UK0tc59H+zYtOWdCfwbsV/tq87c8HMZv9dq7\nXaP//vooaVHEWcf0j3WPRRERkVzW5Fu4Kt32yCt8UMuCn9eePZT2bVpW2deyuCi1gGdjWL1uMx3b\nht/xo9mLaj3uvu+N4cOPN9N9r7aN9rurG3HQF1lZ9gmvv7OuxsffXR0WLB02sFtiMYiIiEj9NYsW\nLoDX0oqLu6eMokVxCL11SRHdS3cvbjZ8uo3VabMBP495r6zi+/e+yAW3P19lYPh908ZUOe7as4dS\nWFiQaLFVKX0s1+DeewFw1NB9qhxzxME9Eo9DRERE6tbkW7hGD+7OcwvfT21PPe1g2rQq5t5Lj6Ci\noqLOWX4bPtlKx2oz+OJYu+EzHnrad9t/7nEDKCwo4KbvDGPZe+s5dMDee1yrqrH9+/D9KCku5JD+\ne9O5/a6/7+mXwvi14qJCSlrUvX6ZiIiIJK/JF1zfPLofp47tw87yclqXFFcpsOqzpMKWbTvpGOP3\nffBRWHPqF39aysSvDeB7M3e/Lc9p4/pw2IDQXde1U2u6Zmmx1fFDd7/h8+VnDOGxZ5fzneMGZiEi\nERERqUmTL7iA6L59DWut2b6zvN7Hbt2+kyt++vfUduXMP9jz8gpNSe8eHbn8G0OyHYaIiIikaTZj\nuOLqWRpm6NW2+nl5RQU7y3cVY1u3VV2tPt0d3z28WRRbIiIi0jTlbMFV2iksuPnPZWU1Pv7jxxcz\n+Ud/5flX36e8ooLzb6+52OpZ2jY1O1FERESkIZpFl2JDrCwLSyM8+eK7nHxE7yqP3fHYqyxe8REA\ns558k1lPvpl6bPTg7nzz6H6ZC1RERERyXs62cB3cpzT188ZPt6V+Llv/WarYqomKLREREWlsOdvC\n1a9X59Qtfqbc9VfGH7IP5RUVqfW7atJBXYciIiKSgJwtuL7cu0uV7criq9LMi0fTskUhBQUFzJi9\niIXL1zL9/OGZDFFERETyRM4WXHWt0VWSdhPoi77+paTDERERkTyWs2O49uS/vto32yGIiIhIHsnZ\nFi6AI7/SkzkLVvLDcw+jU7sSPt2ync+27qBHtEaXiIiISCbkdMF1+pF9Of3IXa1Z6d2IIiIiIpmS\nl12KIiIiIpmkgktEREQkYSq4RERERBKmgktEREQkYSq4RERERBKmgktEREQkYSq4RERERBKmgktE\nREQkYSq4RERERBKmgktEREQkYSq4RERERBKmgktEREQkYSq4RERERBKmgktEREQkYSq4RERERBKm\ngktEREQkYSq4RERERBKmgktEREQkYSq4RERERBKmgktEREQkYSq4RERERBKmgktEREQkYSq4RERE\nRBKmgktEREQkYSq4RERERBKmgktEREQkYcWZ/oVmNg44EVgN4O7XZjoGERERkUzKaAuXmbUG/heY\nHBVaXzKzMZmMQURERCTTMt2lOAx4x913RNsvABMyHIOIiIhIRmW6S7ErsClteyNw8J6eUFraviDR\niJqI0tL22Q6h2VHO4lPO4lPO4lPO4lPO4mtuOct0C9caoEPadodon4iIiEjOynTB9Tegl5m1iLZH\nAE9kOAYRERGRjCqoqKjI6C+MZimeTGjZ2u7u12U0ABEREZEMy3jBJSIiIpJvtPCpiIiISMJUcImI\niIgkTAWXiIiISMJUcImIiIgkTAWXiOQ1MyvNdgzNjZn1M7MRZqbPkHoys67ZjqG5MbMe2Y6hMWmW\nYgaYWRvCDbuXAq+7+ydmVuDuSn4tzKwdMAl42t1fMbNCdy/PdlxNWfQ++w7wNrDA3d/T+6x20b1d\nTyTcXuwN4FF3X5rdqJq26D12LHAU8AfgWXfftOdn5bfoWnYCcDjwFvCCu8/XublnZnYmcBlwubv/\nLhc+A/TtJGFm9hXgh0B74CzgCjNrqxOtTqMJ+ToHwN3LzSwvbvPUEGY2FvgBUA58DTgpukDpfVYD\nMxsC3A28A1xBWIR5cDZjaiZGAmuB84DXgR1mVgyg87NW/0k4L68BKoCpZmbuXqGc7S6t1bQQWAB8\n3cza5cJngAqu5B0GPOzuM4EHgG7A90AXqJqknWx7Ab8COpnZBAAVDzUzs1bAKcAj7n4nsBAobu7f\nBpNgZkXRj+sIxdZ8d38b+AtwULbiasoqcxadm8cTioZTgTOBW4BpoPOzJlHOTgWWuPuHwMOEVq6p\noJxVF7X6VV639iacl5uA082sS3PPlwquRmZmPczsYDPrGO0aQmipAVgMPAYMN7P9mvubp7Gk5axD\n2sm2hfDt5kVgoplNMbMu2YuyaUl/n7n7FqAncLWZHUC4UA0xsx+YWd/o+Lwu7s2su5l9H7jUzEa4\n+wrgzrRzcBkwLzpWY7rYLWejonPzVWA6ocv6KuCPwDgzOyKLoTYZZra/mZ1rZh0gtMwDLwNXRYe8\nD/wOaGdmlqUwm5T0nEWtfkXR7f9WAQ8CKwhDJS6Ojm+21zIVXI3EzFqY2cnAhYQC63dmthcwAxhm\nZn3dfSvhwu6ED8i8VkPOHjezyrzsQ7hQFQE9gO7u/lFWAm1CasjZ76Pi/mTgKeBOYD5wA6Hw+hbk\n9zdpM+tPyNcTwL+A28zsq9XGHvUHXoiOPS0LYTYpNeTsVjM7EvgzcCBwSHToX4CXgO3ZiLMpMbOW\nhN6LEwktgZV+QbiH8NHRebgK+BhYn/kom5aacubuO919OzAcOB0oBV4DiqLP0WZ7LVPB1XiGAMe6\n++XuPplwAbqG0Bz6FKHpHXdfDrQGPshSnE1J9ZyVE8a4dSIUWlOA94CfAkea2XVq5dotZ9uAm4ES\nwodfC3f/o7svIbzHXsxeqE1GO6C/uy9y90cI5+MJZjYIwMzaAx0JF/x7ga3N+Vt0I6mesycJA79b\nEa5rlS02g4BehJabfNcSWATMIXzJPiDavwyYBdxhZiWEYSXFhK7ZfFc9Z/sDRNf5VcCHhDGWrxO+\nVI5szudmcbYDaM6iE+qdqNm4E+FC3Tsqqn5OGMT8OHA9MN/MphKKrYXAR/k4S6WOnD0EXEtocl9C\n6LZYbWaXAK8As/KxlaseObseeJRwUfqymU0iFKxbCa0PecXM+hG+Mc8hvI/WAevNbJi7/43QTTGd\n8MG3BDiSaHIGcL67v5b5qLOrHjmbRfjSuLe732Vm+5rZ9cBmYKq7r8pS6FlTLWeVs89/AnwZMEIB\nf4e7bwPuiZaF+H709KvdfU024s6meuTsBELOPjKze9x9XdSC/y5wVHTNa7a0LEQDmNnewHhgLLCB\nMNZoLuEivoYwK3EkcAbwV3e/zcy6E7p4Wrv7/KwEnkUxcnYmMMfd746eVwKUuvvKbMSdTTHfZ8+5\n+51mNho4FPhL9EGZFyq/vJjZ+UAHwtIYY6KHLyAUDK8AP3P3DWY2A9jm7pea2Qhgn6glJ280MGc7\n3P3iaDB4y2j8YN6oJWejgbbuflbacRcRWv/ucPc30vYXu/uODIedVQ3I2Z3u/nr152c47ESoS7Fh\nziG0HpwHPAP8mNCFeANQBkwkDJC/uvIJ7v6+u7+Sj8VWpL45u4rQPVZ5om3Nx2IrEud9VgTg7s+5\n+y35VmwRWo4htAA+5e6PAf9DKOCHEma8HsSuCSyvA88DuPsL+Vhs0bCczYMwGDwfiy1qztlVhGVY\nxqcd/mtCd/+tZnZhNFaJfCy2iJ+z6dVylhPFFqjgqrdoEClm1hk4Gvhn1FT8HLASmBl9k7kJuJ8w\nBuI/gGezE3H2fd6c5dKJVl96n8VjZsOA2wkfbAMJ35z3BYi6n68B7nL3p4GfAYeY2Y2EsUjPZCXo\nLFPO4qtHzq4Gbk17ShGhR2Mh8FB0DucV5Wx36lKsQ1Rl30BY52isuy83s18RqvVTov9OIMzoOYkw\nhXUyoT/6Rnd/JxtxZ5NyFp9yFo+F1buvIQxIfgy4j9D9tR6Y5O79ouNKgN8Dl7r7kmjmcJG7r85K\n4FmknMUXM2e/Baa5++IoZ63ysXVeOaudWrjqVkR4s/yGXQMeJxJmT0wlTCGfQ5jd9GnUZHyfu5+b\nbx+CaZSz+JSzeCqn189x93WECSpDo7F/O8xsSnRcF8Jte94AcPe1+Vg4RJSz+OLk7E1Ct2tlznK2\ncKiDclYLFVx120ZYA+RRYFC0fs9mwofhDHe/BfgC0J0wswd335CtYJsI5Sw+5SyezcBsd38rg5oT\nNQAAAuxJREFUbV/luLUrgf5mNp0wDm6Bu+/MdIBNkHIWX5ycvaycAcpZrbQsRB2iN8OrFm6f8n+E\n1W6f8XBfp6FmdgKhz/mW6AMy7yln8Sln8UTj+95L27UvUYsMYW2fGwkLJr7tebiUSE2Us/iUs/iU\ns9ppDFcM0aJsdxHWNnqEsFrwF9x9aVYDa8KUs/iUs/jM7FxCnk4izOz876g7Q2qhnMWnnMWnnO2i\nFq54yggD/04hrHu0FFib3ZCaPOUsPuUsBjPrBlxGdK9Sd/9llkNq8pSz+JSz+JSzqlRwxdODMOvi\n7FycspoQ5Sw+5SyecsISGbd6uF+p1E05i085i085S6MuRREREZGEaZaiiIiISMJUcImIiIgkTAWX\niIiISMJUcImIiIgkTAWXiIiISMJUcImIiIgkTOtwiUizZ2bDgeuBAcDjhPtOtgVmuftv6njuN4Ej\n3P1biQcqInlLLVwi0uy5+3zgQWCFu1/g7qcC3wauNLPJ9XgJLUgoIonSwqcikhOilqrz3H142r7x\nwG8ILV/3AEuALsDL7n6vmfUGZgLdgbnAH9z9GTP7LtAH+AzoRLj/W97fNFxEGk5diiKSy/4BtAG6\nEm4v8hyAmb1qZr939+Vm9gtgtLtfFD02FjjO3b8abV8HTAOuzspfICI5QQWXiOS6AsLwiTFmdhqh\n1aozcCDwYQ3HHwN0MbN7oud2AT7IUKwikqNUcIlILhsKfAKMAwa7+wkAZjYYKNrD8/7m7hdWbphZ\nm0SjFJGcp0HzIpKTzKwbcDOhK7AL8HG0vxDomXboFqLiy8zOBJ4itIYVRvtOAOoz8F5EpFYaNC8i\nzZ6ZHQZcBwwEZhOWhegAPOTus81sH+BhYBmh8DoOWAScQxjjNRtYDvzZ3WeZ2UXAcOA9oBVwibtv\ny+xfJSK5RAWXiIiISMLUpSgiIiKSMBVcIiIiIglTwSUiIiKSMBVcIiIiIglTwSUiIiKSMBVcIiIi\nIglTwSUiIiKSsP8HZ4GPRfvZN/sAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119ca6c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = pd.DataFrame({'SX5E': es['SX5E']})\n",
    "data.plot(figsize=(10, 6));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data['R_n'] = np.log(data['SX5E'] / data['SX5E'].shift(1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SX5E</th>\n",
       "      <th>R_n</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2015-12-23</th>\n",
       "      <td>3286.68</td>\n",
       "      <td>0.022262</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-12-24</th>\n",
       "      <td>3284.47</td>\n",
       "      <td>-0.000673</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-12-28</th>\n",
       "      <td>3256.49</td>\n",
       "      <td>-0.008555</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-12-29</th>\n",
       "      <td>3314.28</td>\n",
       "      <td>0.017590</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-12-30</th>\n",
       "      <td>3287.98</td>\n",
       "      <td>-0.007967</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               SX5E       R_n\n",
       "Date                         \n",
       "2015-12-23  3286.68  0.022262\n",
       "2015-12-24  3284.47 -0.000673\n",
       "2015-12-28  3256.49 -0.008555\n",
       "2015-12-29  3314.28  0.017590\n",
       "2015-12-30  3287.98 -0.007967"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "## np.cumsum calculates the element-wise cumulative sum of an array/time series\n",
    "## np.arange(N) gives an array of the form [0, 1, ..., N-1]\n",
    "data['sigma**2'] = 10000 * 252 * (np.cumsum(data['R_n'] ** 2) \n",
    "                                  / np.arange(len(data)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SX5E</th>\n",
       "      <th>R_n</th>\n",
       "      <th>sigma**2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2015-12-23</th>\n",
       "      <td>3286.68</td>\n",
       "      <td>0.022262</td>\n",
       "      <td>446.280005</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-12-24</th>\n",
       "      <td>3284.47</td>\n",
       "      <td>-0.000673</td>\n",
       "      <td>446.220423</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-12-28</th>\n",
       "      <td>3256.49</td>\n",
       "      <td>-0.008555</td>\n",
       "      <td>446.185389</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-12-29</th>\n",
       "      <td>3314.28</td>\n",
       "      <td>0.017590</td>\n",
       "      <td>446.230025</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-12-30</th>\n",
       "      <td>3287.98</td>\n",
       "      <td>-0.007967</td>\n",
       "      <td>446.191722</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               SX5E       R_n    sigma**2\n",
       "Date                                     \n",
       "2015-12-23  3286.68  0.022262  446.280005\n",
       "2015-12-24  3284.47 -0.000673  446.220423\n",
       "2015-12-28  3256.49 -0.008555  446.185389\n",
       "2015-12-29  3314.28  0.017590  446.230025\n",
       "2015-12-30  3287.98 -0.007967  446.191722"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlwAAAHQCAYAAAB0hrSOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xl8U1X+//FX0r1QoEJbFwTE5YKCituAoKCOqKDjuIw7\nuOEPREUR3BjFHVABHdHvOC4oIi6D4qAgOrgiigvigoNcFzYFpAUL3bckvz9u0ps0SZu0TZuU9/Px\n4EFzkzQ3J7f3fvI553yOw+PxICIiIiKx42ztHRARERFp6xRwiYiIiMSYAi4RERGRGFPAJSIiIhJj\nCrhEREREYkwBl4iIiEiMJUfyIMMwDgIuBMqB44G7gF+AacA64ABgkmmaBd7HTwQ6AJ2ApaZpvund\nfhhwDbAeyAUmmKbpbsb3IyIiIhJ3GsxwGYbhBGaapnm3aZoPAlcCG4ApWMHUA8BCYIb38ccAQ0zT\nnAyMB2YYhpHl/XUvAH83TXMq4AIubeb3IyIiIhJ3IulSPBpwGIZxnWEYtwJnmKa5HRgOrPA+5hNg\nmPfn033bTdN0AT8Agw3D6Amk+7Jg3ucMb563ISIiIhK/IulS7A70B843TbPEMIy5hmFUAzlAsfcx\nRUC2NxuWC6zxe36Rd9t2v8f7bxcRERFp0yIJuIqAtaZplnhvLweGAPlAlvf+DkChaZpuwzB82306\neB+b7/257vZ61dS4PMnJSRHspoiIiEirc4TaGEnA9TnQ2TAMh2maHqyMl4k1gH4A8CowCFjsffxi\n4A4AwzBSgF7AMtM0iwzDKDMMI9c0zXxgoN9zwiosLItgFxNbTk4WBQXFDT9QaqnNoqc2i57aLHpq\ns+ipzaIXz22Wk5MVcnuDAZdpmoWGYdwC/MMwjAKgC3A3kAlMMwzDAHoCE72P/9wwjA8Mw7gfa5bi\nBNM0i7y/7hJgimEYG7DGj81pypsSERERSQQRlYUwTXMh1kxEf5XA6DCPnxFm+3fAqGh2UERERCTR\nqfCpiIiISIwp4BIRERGJMQVcIiIiIjGmgEtEREQkxhRwiYiIiMSYAi4RERGRGIuoLISIiIhIvPrP\nf17jl19+Jjs7my1bNpOdvQcOB7z88jxGjryCUaPG8J//vMZbb73JpZdeycCBxzF69OWkpaUB4HQ6\neeSR/6Ompob/+79/8MYbr3PxxZfi8XgA+Oknk6lTQ1a8ipgCLhEREUlYZWWlPP30EyxatBQAt9vN\nzJkPMnHirbhcbtav/wWAoqJd3H33FPbaa28A+vc/lssvvyrgdyUnJ3PeeRfx3/++HXDfJ5983OT9\nVMAlIiIiTXbXXWm8+WbzhhVnnFHDXXdV1vuYlJRUAF55ZR6nnjqcjh07MXHirQCMHn0No0aNYPr0\nqRx++BG1wRbAL7/8xIsvPk9FRQW9ex/MgAGDQv7+6dOnMnHibU1+Lwq4REREJGGlpKTw2GNPMnfu\ns8yd+xzdu/dg5Mgr+NOfBpCamsro0dcyefKtjBhxecDzLrnkMnr1Ohi3280111xFZmZ7DjvscADK\ny8uYNWsmHo+HTZs2Nst+Onz9k/GqoKA4vnewGcTzIpzxSm0WPbVZ9NRm0VObRU9tFr1wbebxePjw\nw/e4//67WLDgLdq3b8+DD95Phw4dWLPmfzz22JMhf98TTzxGeno6l102it9/38qoUSNruyg3bdpI\nt27do9k3R6jtmqUoInGjoMDBggXJxPn3QBGJI7//vpVp0+4FwOFwcNxxQ7yD4T289NJczjvvQkaP\nvpaqqipefPF5ADZt2sCiRfYS0b/9tom99+4K4B0ob5+EunXrzqefLm/yfqpLUUTixvnnZ/D990ls\n3FjJOedU89ZbyQwdWkNqKnTtqihMRIK1a9eeoqIiZs16mHbt2vH771sZPfpaXnnlRVatWsmgQYNJ\nSkrCMHrz9NP/wuVycdppZ/DZZ5+wY8d2SktLyMvbk6FDT6WmpoYFC+ZTWVnF88/PBqwAbPXqbzn2\n2NBjvCKlLsU4oHRy9NRm0UuENsvNzQp7X36+ve9btjjIyPCQnR3b/UmENos3arPoqc2iF89tpi5F\nEUlon32WxM6d1s+HH94ewwgfnImIxBt1KYpIQvjLXzIBWLastJX3REQkespwiUhCWbYsqbV3QUQk\nagq4RCRupKU1PGSzuroFdkREpJkp4BKRuOFyNfyYNWuU4RKRxKOAS0TiQmEh1NSEnNwTYP78lNqf\n16zRKUxEEoPOViISFxoz63DixPQY7ImISPNTwCUiCWvtWp3CRCQx6GwlIq2upKRxz7v44mo2bXLw\nww86lYlIfIuoDpdhGCuAcsAB1JimebJhGNnANGAdcAAwyTTNAu/jJwIdgE7AUtM03/RuPwy4BlgP\n5AITTNN0N+9bEpFE8/77jSsJ6HDAX/+ayW+/Ofnll2KyVAtVROJUpF8Ll5imeaJpmieYpnmyd9sU\nrGDqAWAhMAPAMIxjgCGmaU4GxgMzDHtwxgvA303TnAq4gEub642ISOJq1y66FbzuvLMCgOJi+O03\n6zT2+OOpzb5fIiLNJdKA61DDMG4yDONOwzCGebcNB1Z4f/4E8G0/3bfdNE0X8AMw2DCMnkC6Lwvm\nfc7wpr4BEUl87drVf3/Hjh5uuaWy9vbee1sB2rx5dpA1c2ZaTPZNRKQ5RBpwTTNN8yHgXmCSYRjH\nATmAb+XIIiDbMAwnVleh/4qSRd5t4baLiNT66KNSBg2qCdi2a5eDCROqam9nZ4fOiJmmxnKJSHyK\naOCEaZorvf+7DcP4GDgByAeysAKnDkCh937fdp8O3sfme3+uu71e2dmZJCe3/UKHOTkafBIttVn0\n4rXNfGOv7rwTjj++HffdB0OG2Pefe66176tWwXvvwYknZob8Pccd1w5PdL2TDYrXNotnarPoqc2i\nl2ht1mDAZRiGAQw0TXO2d9OBwAJgMTAAeBUY5L2N9/87vM9NAXoBy0zTLDIMo8wwjFzTNPOBgX7P\nCauwsCy6d5SAcnKyKCgobviBUkttFr14bbM1a5z89JMTyKCyspKCgioOPhjy863A6vvvkygurqGg\noJyuXeHSS6GsDAK/19m2bCkmJSXkXVGL1zaLZ2qz6KnNohfPbRYuEIwkw1UEDDMMYy+gI7DJNM0X\nDcNYAkzzBmQ9gYkApml+bhjGB4Zh3I81S3GCaZpF3t91CTDFMIwNWN2Zcxr/lkQk0e3aBUOG2AO4\nkuuckY47zsX33yfRt2/gmj/p6dCjh5sNG4K7EKurabaAS0SkuTQYcJmmuRU4N8T2QmB0mOfMCLP9\nO2BUlPsoIm1URUXgUj5JSYH9gZMmVdK/v4sTTwwc0wUwd245xx0XPNpei1uLSDzSCFMRaTU1deKo\nuhmutDQ47bQa0kJMQMzICD1Ya9s2ndZEJP7ozCQiraawMDDDVTcAq09GRujtgwa1Izc3i9WrdXoT\nkfihM5KItJpvvw2cgfzee5FXnA+X4fI56aQGinuJiLQgBVwi0moqKuredoR+YAiZfpUhbrqpMvwD\nRUTigAIuEWk1VVWBt12u0I8Lxel39hoyJIq+SBGRVqCAS0RaTXV1YEbrkksaP8Xwnnsqgra53Y3+\ndSIizUoBl4i0mroZrgsuiC7gmjWrnAEDajjsMHfQAHyAtWt1ihOR+KCzkYi0ml9+sU9Bq1eXRF2w\n9Pzza1i4sJzUVPjTn4L7Ix94wF7c2uOBl19OprCw0bsrItJoCrhEpNW89podYSU1ccnUE05w8cEH\npZx3np0l693b7lN88cUUxo3L4Morw9STkIRSUgJnnZXBkCGZTJuWygsvaHkBiW+Rz8EWEYmhpi46\n7XDAIYe4eeyxCk47rYbLL8+oLaT6668Oxo9PB2D5cp322oKXXkrhk0+sz3LNGitab8oYQJFYU4ZL\nRFrFq68GBj6OyCtCNKhbNyuztX69dYq77rr0gPuLioKeIgnm739Pr/f+b75xct116axb54hq9qtI\nrCjgEpFWsWKF3Yd4zTVVdOnSxBSXn65drYCrtNS6XbfA6hNPpNZ9iiSQjRtDR+effWZ9ztOmpTJ0\naDteeSWF/v3bs9deWRx0UPuW3EWRIAq4RKRVdO5sBVi9e7u4887mLVya6o2n3nvPGiRfWhp4gf7h\nB536EtXOnXD00aGDp5IS6/+ZM4MX39y5sxlTqCKNoLOOiLSKTZus088DDzR/lXjfYteVlQ7GjAke\nJJ+V1ewvKS2kT5/wmaq0NNi8OXxg9fjjGlgvrUcBl4i0igULrItfc47d8kn2Gx72wQf2jUsvtQp/\npaY2X/eltKyqquAD5rTTrMHyl12WwbnnZgbd7/PQQ8GZL5GWouk6ItKqduxoua6e666rYs6cVMrL\n1b2U6G65pZKDDnJTVQUFBQ6WLEmhuNhBcXH4zzY7W4G2tB5luESkxdX4LX3Yq1fLTSHL8PYuzp+f\nwj33aOB8ovE/bm64oYozzqjhnHNq2Lw5+FJ2+eVVQds2b3Y2ufyISGMp4BKRFudfpLJnz5a5Ah56\nqIuMDPu1HntM3UuJwOOB3NwscnOzmD7dDpL9C+UWFQVntS6+OHRNrg0blN2U1qGAS0Ra3PbtLX/R\nmzSpknbtWvxlpYn+8hd70oNv9qFvLJ7PvvsGr1KenAydOgUH8x9+qJE00joUcIlIi2uJQpQTJwbO\nfkxPj80AfYmdV15J5vPPgwOkAQMCD6AxY4K7D6uq4LLL7O2nnmplvFQSRFqLjjwRaXG+WYTTplXE\n7DVuvjnwItyxowbvJJLVq51cd13odS9zcwM/y/YhKkVkZXlqA7Fbb62s7WLs0SM4GybSEpRbFZEW\n5xuL06dPyw2Y9xValfjm8VgrBJx0Uvj+3169Gg6a9t/f+rzz84sBeP99a9BXdbXSnNI6Ig64DMNI\nBz4H3jFN82bDMLKBacA64ABgkmmaBd7HTgQ6AJ2ApaZpvundfhhwDbAeyAUmmKaprxsiuxmXy7ro\n7bNPywVBeXnWa82cWcGNN1rr8M2Zk8LIkdXqaowjF12UwXvvBV6ajj22hk8/tbeFGps1YkQVc+da\ngfzUqcGZU9/qA1XBvY8iLSKaLsX7gFV+t6dgBVMPAAuBGQCGYRwDDDFNczIwHphhGIavrvMLwN9N\n05wKuIBLm7j/IpKATj7Zmt/fkt18vqDKf/baTTels2CBEv3xorKSoGALYPp0O4A6/fTqgMK2Pk7v\n1axLFzdXXhk8QzHFOzHWv7SESEuKKOAyDOMSYDmwwW/zcGCF9+dPgGHen0/3bTdN0wX8AAw2DKMn\nkO7LgnmfM7wpOy8iiamoCBwOD5nhi4I3C6czOKCrm8169FHV44oXM2cGfhZdurhZvbqkNjsFweti\n+pxzjhVJjR8fOoWVkmIdC6Eq1Yu0hAYDLsMwegO9TNP8T527coFi789FQLZhGM4623335dazXUR2\nM7/84iQnx1OblYiVjh0bfoxpau5QPFizxsnDDwfWRnv66Qry8jy1a2MCAbXU/PXv72LjxmKuuip0\n/S1fhqs69N0iMRdJLv0soMIwjFuAQUCKYRjXA9uALKzAqQNQaJqm2zCMfO92nw5AvvdfhxDb65Wd\nnUlyclJDD0t4OTlaTTdaarPotWSbrVgBxx4LN90EDz5ob6+uhu3b4cQTY78/bu8I0XHjwr/WVVc5\n6t0PHWfRa0ybDRkSvO3oozPJyYHsbHtbdXUKOTnRL0K9557W/0lJqeTkxF9WU8dZ9BKtzRoMuEzT\nnOL72Ttwvp1pmv8wDMMABgCvYgVii70PWwzc4X18CtALWGaaZpFhGGWGYeSappkPDPR7TliFhWVR\nvqXEk5OTRUFBccMPlFpqs+i1dJtdfXUmkMRDD8GNNxbXVgbPz3cA7UlJqaGgoDym++DxtAccVFRU\nUVDgX5fLPlEvW+aioCD0eUbHWfQa32bBF0+Ho5iCgsD7O3aspqAg+nIi1hqL7SkqqnsstD4dZ9GL\n5zYLFwhGnEs3DONs4Digv2EY5wOTgJMNw/g78FdgIoBpmp8DHxiGcT/wCNZMxCLvr7kEmGIYxu3e\n157TuLcjIvHuoIPsCchlZbBtm4MdOxwsXWp9z/vqq9h35YVbN+/22+0L7g8/JFFQoHE9sVRYCM88\nk8Lq1aE/85077Z9XrSqhTx8X++3nDhgc37mzdTy1b9+4iRb2LMXgz9rlUlejxF7E03NM01wALKiz\neXSYx84Is/07YFTEeyciCammxlog2mfDBmdtXSVfsdO//S3208WGDavhlVdSOOKIwHpfV1xRxX33\n2QODzjwzg08/bfvZ9JZWWQn77hv4bX/z5uLa8VQ+S5bYl6KuXT28/35ZULA8d245t9+ezg03NK6u\ng+81589P4YQTajjuOBd5eR4efTS19lj47bfigAH6Is1J86FFpNn5X0ABLr/crhjum5Z/1FGxL3r6\n0EMVXHJJNcccE/hadSuT//xz4DjRlSudFBQ4+fFHuOyyyAbfS6BvvnEydGhw8dKiIkdAEdqVK51c\nf711fBxyiP051Z1NetRRbt5+u/FBsW+WIsDYsRk4nR7efLMsIPDeudMRVMVedk/LlyfRrp2Hfv2a\nr1SoAi4RaXZbtgReLTdtsruS/vMfK9WQmRn7C1t6OvzpT6EDu6++KuHII4PXhPn5ZwfDhtmBwvLl\nGcyfX85PPzlZtCiZ0aOrYl7Ooi0YNix0I5WWQufO1s9btwa29ZAhsQvC62au3G4Hw4cHBoRlSnIK\n1jF69tnW8etbqaA5aD60iDSbCRPSGDkyncrK8GOiVq60skl1u5Va2r77hg74jj02MAj76KNkPB4Y\nOLAdU6em0aNHYs2Mai01NaGPAf/CoyecEBiUjR0buzLwkRxvs2erP1Gs8aY+33zTfGGSAi4RaRZr\n1zqZOzeVt99OCeimCaclMlwNOeuswJHS4QbZv/xyYGfAqacqxVUf37qFofzxh30xq7u0U05O7I6J\nSAKuJ55QwCXQv7/9pStUt3hjKeASkahVVVkzu/wdf3x0J6ajjmr9ZVTvv9+erVhWBv/+d+hRFr4x\nRj6rVrX92oBNccEFgQHptm12t4yvC3HBgmRWr7bb8dprY1uqIdZFdqVteOed4L/tIm+dhaoqqIi+\nIkktHYIiEmDevJQG1xfs2jWLY4+1A6xwJ6HLL4/vlYK7dLEzKm43fPBB5MNaNd4nmMtF0DqHa9aU\n4HDAjTfaAdWDD6YyZowdxK5fX8zkya13rNx8c3zV5ZLWc8UVGUHbDjggiz/+sM573bplkZubFTYb\nXh8FXCJSq7wcxo9PD7gYhrN+vX36mDUruCvmuONq6N/fToPV7b6LF717W/tYXR2+SzGU339X7a66\nVqxICsh8fv55SW1Q26uXndGcPj2wy7ld8/XaNMqIEdX06+cKu2yQ7D7CTbJ57LHAc9ymTdH//Svg\nEpFa/uNrwvEPSubNS+Gbb5w89FDwmK2PP04OuPiec041V14ZfxmvAw+0AoGqKgevvx75SP5XX01p\n1Lfctsw3swtg2LBq9tvPbqBwa1beemvrZpeOO66GvDwPyclQXq4gendWUwPLl1sp2k8/LQm477HH\nAs9xjemiVlkIEam1c6d9wamqCp5KD4Hdh+PHp4f9XaeeWl27liFAWZmDqVMr+frrJPbcs/XHb/n4\nusC+/77hM+ihh7r47jtrjMf06WmkptLoQpxtXUVFYPDiC2zruvHG1m2/adOsgG/HDmt/161z0LOn\nIund0Vtv2SFRhw71PJDA2baRUoZLRGr5dw1u3x762359g0b//W97YNPs2RWcfrp9Vlq71jrdLFlS\nxnPPNWHkaTPzBVz+U8HDuemmSpKS7Ivx22/rO6vPf/8bONi4bnu2RKHbhlx6aRUXXRQY4O2zjxUI\nrltnHZ/+M9Rk9/Lss3aGu2PH+oPucGVP6qOAS0RqLVhgn3Buvjl09qpu5sJf9+5u8vOLyc8vJjmZ\ngAKhw4dbwVfdCuKtzVeB/IYb7HFry5eXsnp1SVCXYUYGLFhgL7it2YqW6mq45JLAmYknnBCYAsjL\na/2s0UMPVfLII5W8+KL9xUBFbMXHtwJF374u0tJgxIjw2dfS0sDb//hHKnffXX85HAVcIlKrTx87\nC/Hdd6FPD+XlITcDsPfewRfVCRMqGTasmr5946cb0V9SiJgpN9cdMkDo1MkTMBEAohto39Z8/bWT\noiL46iu7EX/+GT7+uJTbbgu8WKWlwaxZgQdPTk7rHBOhjsV77rGyrg1lNqTtatfO+uznzLGO0xkz\nKtm0KXSl+aeesnsDli1L4v7703j88VQq6xmSqIBLRKiogEmT0vj+e/vCef75oWcV1pfhSgvxBe+W\nW6riqguxrlDj1Pxnzb31lv1VNjvbE5Shqy8AbctWrEjilFPaMWZMBn/5i50m2n9/MAx3yEKj/uO4\nHn20nPnzW6fx0tKCg6qLLrKO9127HOzcCZdfnh7RuD5pGzweO8Pv/2UrvU6iPzfX7d1uPaaoCM49\n1z7+CwvDnx91NIkI3bpl8fTTgZHH/PkpIWtNhRvD9dtvzbfmWEvq0SM42+FfS8q/QGt2tnWSnTrV\nboTdtVvxzDOti8y779qN1VDx0iOOsNvyggtqOPjg1slwhepGzPCrhDJuXDqLF6dw4onteP11jdPb\nHRx1lP0tq75VCQ491DpmfcfLAQcELvVVVc8cEAVcIhLSli1ObrsteBxXuKnzoTJFiaDuN1gIHmf2\nxhtlPPpoee0YjyuvtLN/77yze12Q33kniXXrQh8DkRQvPeooF/vv37rdy6mp8M47pXzzjT313/8i\n+/bb9o3RoxuuSSeJ7Y8/4Ndfw4dDa9faXyZ9XYbhAisFXCISZN06B2PGpLN5c+DF87zz7GDiww+D\nsze+xaf9vfZa4pZdr1tPx38ZGp/+/V1ccEHgIHDfbLdDDmn92Xct5fnnUxgxIrNJM/kWLy5j+fLS\nhh8YY/36uUOOOZTdz/bt9YdCe+wBe+3lq9dHwP91LVoUPj2mgEtkN3X11RksWJBCv36BF89qv6Fb\noWrNfP118GljwIDEDTqczsCLbqSzKOsOnm/rysth4sTwdddefz2yoNvhCD1RQaS5VFdbXYR9+rSL\nqF6W/0D3+fNDH8e+Y9Y33KCqyjpR+Faq8JkyJfxMRQVcIrupcEvT7Nplby8oCDxFFBfbAckLL5Rx\nxx2VvPlmWdD6eYnEf4bdgQdGHkT5irp++eXuET3UHeNXV1sOQOsu1C7xbdmyJDZtcpKf72Tvva0x\nVv/7n5Nzz83gzTftk9UnnyTxzDMplJVZJ7Xrr69k8ODQH7avG/yAA6z/X301hR9/dPLDD9bf/8MP\nNzwxSAGXyG5q69bQf/7du4ceX1NZCfvvn8XixVbK/IQTXFx3XVXYtccShX/x0p9+ijx4+ugj63lz\n5ybo4LUovfNOcNu88IKdDWgLWatnngk9a/LGG8Nn9iQ+VFbaxZpDfTmYMSOVZcuSufLKDHbutLL3\nZ52VyW23pfPzz9a5sH09PeWPPVbBbbdVBqyMMGiQPdDeV0C3Pgq4RHZTf/5zYK69Xz8rcPIfEO6v\nuNjOfGVmeuqdyZNIGltHa+TI+FyMOxZcLvjiCyvAnDTJ7n8ZOtQ6ZnzjWxLdGWfYfxNDh9o/v/RS\nGznY27D/9//SOfjg9uTmZvHee4Ep93PPzQjIZJ91VmbtyheAX8AV/mSQl+dh/PgqOnQI/ZjMzIZP\nJAq4RHZT/tP5Ad55p4z8/GIOOij0xXPlSvt0Ee6kk4huvdX+xnrqqZEHUf4z7cItzNxWdO1qf/W/\n+uoq+vZ1MXeuld365ZdiPv209QfBNzdfIVSJT1u3wvr19pfAJUvCB8XLliUHZPT/97+kgMk/jz9u\nZcTCZff9hZuNXV92zKdtnyVEJKS647f22y/wRPPQQ9bFpksXe7v/WKW2FHB16WK/l1tuiXwh5T33\ntJ933HHtIlqLMRFt3uzA5bLfW1oavPdeGaecYmW3srICC8WKtIS994Y//ak9I0emk5ub1fAT6ti5\nM/jv1f9vOpxQ41UXLSpljz2U4RKREOpWR6/brXbppdV07uxm+3YnJd5SRYcfbgdfbWG8jo9/IVdf\n9ejGWL8+8U+nO3Y4mDQpjQ0b7IuR/yxW/262turQQ61AMjfXw+mn2xnPumvnSet55RU76vGvmebv\nyy9LmDEjMEvZtat9Dgs1mzCSL5KhZjEffbS7NuDq3Dl8lqzBuUWGYTiAN4HPgDRgf+ByIBOYBqwD\nDgAmmaZZ4H3ORKAD0AlYaprmm97thwHXAOuBXGCCaZpto/NfJIH4j8eC0OOYduywAohrr03nuecq\nAoI038yctsDtdwZqSvHWRF9T8cMPkzjvPKsEu2/Q8bJldpSRm+sOO6i8LXnrrTJ27XLQvn1gUdyn\nnkrlhhsiz4C2tuJiKCtzxMWi4c1h1y6466405s1r+I80P9+qpTdiRDWm6eTJJ63nXHZZNffdF75s\nQ2Mz9w6Hde748ssSsrI8QOiMW6RfyT41TfM+0zTvwAq0zgGmYAVTDwALgRkAhmEcAwwxTXMyMB6Y\nYRiG79VfAP5umuZUwAVc2qh3JyJNUrc6ek5O+BPNsmXWY0Ol4NuC00+3szZNCbjcCf7V0Rds+Tv+\neLuv8LvvSkOuldnWpKbafw/+GU//Qdfxzu22ZhT37du+TZS0qK6GAw/MiijYevrpwC8FvowlQJ8+\nrpDraPpkRd8zGaB7dw977BH+/gYDLtM0PaZpTgEwDCMZ2AdYCwwHVngf9gkwzPvz6b7tpmm6gB+A\nwYZh9ATSfVkw73OGR/l+RKQZPPSQdeXs37+GESOq+Oc/w2cuSkocfPedk9tvt7/uX399/WvmJRL/\nLEZTuhSr2/CkxcGDa4Iq8u8O/APMWC1kvW2bA4cD5s0L7BqbNSs1YKJKNKZMsQOT//3P+h2LFiXz\nzTeJ+SEefXRkgwTvvLOCv/wlsNt7yBA74MrK8nDkkeEj0EiHSnz2WQn9+0ffvR5x6xuGMRSra3GR\naZqrsLoEfWtgFAHZhmE462z33Zdbz3YRaWG+EhAzZlQyY0Yl3bvXH2i89VZgRsx/Zl9bEm2Ga+RI\nux0iqWiFufC1AAAgAElEQVQdjwoL4Yor7KjTd2z4Gz++bX7eDfGfTBKrenNHHmkFE+PHp9cuF3Pj\njWnce28aw4ZFPxvB44FHH7UjxZNPzmTMmHSuuCKDoUMTc3ZDt27B6eMzzwx+3BVXBH/r8Z8Uc/TR\nbj791D6X3Xxz47449uzpYeZMa3zYqFGR/21EXB/aNM3/Av81DGOOYRhXA9uwOiqLsMZrFZqm6TYM\nI5/ADswOQL73X4cQ2+uVnZ1JcnLipHIbKyenibnM3ZDaLHq+Nvv6a+t2v37tale9r599Al+8GPbc\ns222fdeuWUGZnPqOM//ZeRkZmeTkxGjH6jFuHMyaBRs3Qrdu0T23shJy/b72OhywalUSGzdCjx72\n9v79o3tvbeVv8+abYdo0KCmBc89NISen6fW43n4bLroItmyxsqv+a/J9+mkW554LL7xgb+vQISuq\nrtxPPw287fE4WLDA3u/OnYOP8XhWUGAd22B9Dr7yCwsX2o/54gsr0OzWLfRxt2YNdOoUfFyOHp3G\ngw/CJZfAI49YbROpnBzfuM1U77+GRTJovjewn2mab3k3rQf2AxYDA4BXgUHe23j/v8P73BSgF7DM\nNM0iwzDKDMPINU0zHxjo95ywCgsTd1HcSOXkZFFQELxgroSnNouer81+/NEJWJFCSUlx7SzEuvr1\ny+Trr60vOx5PJb6g64gjiikoCP2cxGWdaHfsCDymGjrOkpNT8bXLH3+UU1DQsmmu115LZtYsK2J+\n8MEqrr22is6dG+4Wdblgr72CLy633FJJQYEvArDuP/HEGpzO8og/87b2t3nvvSmMH5/ebJ/vaadZ\n7ZqRAZ06eQB7bKTLVcZhh6UBdpLhvvsqGTcu8izK4MHtA35nXWPHVnHvvYkxJKC6GvbZxz5Oy8qK\n8R2XDgf8+99lrFyZRI8eVvuEO0a7dMHvfvv3ZWUV89tvVmbb7Q7//GiF+8IRSZxbCVxhGMYkwzDu\nwgqgpgN/B042DOPvwF+BiQCmaX4OfGAYxv3AI1gzEYu8v+sSYIphGLd7X3tOo9+RiDTKww9H9m3s\nscfsKdUPP2x/xW5LJSGa6rrr7Avhhg1OfvzRGVBmIpZyc7O4+mo7Pfn446n07t2ea65peBmaBx4I\nPga6dXPXdh1mZsLLL5dx9tnVzJ7d9mcm1icpyQpgm9plXFVFUL2ouhNRHA5YvTrwD6yhchRPPZVC\nbm4WzzyTwtq1TmpqrN95+eWhg7R//SuV335z8NVX8Z/m2rgxOHB8/nkrCbNlCwwe7GLChOi6uwcN\nCvwgmzJRJloNZrhM01wHnBvm7tFhnjMjzPbvgFER752INLtILxx1i6ECPPigqm/769QJbryxkpkz\n03jssVTuvdcKTH3T0mNl3brwGYz581N4/PEKKipg40YnhhH4OVZUwCOPBPZRrV5dElQ+4MQTXZx4\nYhuY4tZEviWsfIFMY23c2HCA8+23drCVmemhrMzBgQeGn/76668O/v53K8C+7bbAQHv8+CoKChws\nWhTcDXr88e0oKXHw9dcl7LNPfJSNKCy0ugt97X3RRRkBq2E89pgV+J96qov8/GJvJjX61zn2WBfL\nlyczdmzLj0uM/xBXRJqVb0mahmYaJicHVpoHqxhkW7R6dQkrV4bpW21Ar15WGxUWtlzZjGeeqf9r\n+bZtDrp1y+K449oFrBn37bfOgHEud9xRybZtxW2mVlMs+CqLN3UWaqjFv32uusr6f+pUKxDef383\n119vBQT+sxfLy60s2amnZrJpkyNk8U6fzEwP5eWhj8mSEmt7vBTrffDBVAwjq7b7cOtWR0CwNX16\nBeed1zzd9ePGVTFvXhm33dby3arx0doi0mJmzrRO0mee2fAJbPv2wFPEqacm6FS8BuTleejWrXFB\nR2sMQH7qKTvgOuSQ4CxU3752dfjnnrMu2Bs3Ojj55MBZatddVxWycrbYfAFXU+pZLV2axD33hO/q\n7dgx8PYVV1Tx8svW5/bJJ8l4PNYAbd+izKtWJXHUUe157bXwg/gzM+3uyCOPdPHDD8FfKL77Lj5C\ngOnTAwPHceMC26q+LF+0UlPh5JNdrVJTLj5aW0RahH819HCLVNcnkWY3tZSWDlj8My1vvFHG9On1\nd/POnm0FZ0cfHcHquhIkOdn6o7n99nQee6xxsxT/85/wz3vmmXKuuCJwW4cOHqZOtT/XBx5IJS8v\niyuuiGhKMWAFir5u0MxMD507e4KWnbnrrnQ2bWq5A3jXLnj00VQKC2HtWie//ebgk08CM38eD3z0\nUeBop8MOaxtd2zp9irQRkSwtM3my/bUu2sGiEycmxsymeFD3ItKcbr/dl6Gspn9/FwcfbF9Eb701\n9Gd05pnBF+q+fdvGRSzW/Bcrri9LVR//JWP8g4fnny/jjDNqAorvgpWdOvZY+3G+rHQ4p5xiZ54n\nT67gqqus7kin03pd37lhzZrgEfjLl7fMLJgtWxwceGAW992XxmWXZXD88e044oj2zJ8fGFwtWhQ8\ntDwzeBGEhKSAS6QN+P13B3l5WTzxRP3fwP/1r8ZPyalv+Z/dWajJBWedZV8hfN1BzWHZsiSefdb6\nDEeOtFJd/nXU/vgjdLZixYrAi9iIEVU8++zuPfswUsl1rv/Rdi2uXesMGHO3dGlZ7YoG++9v/b/f\nfoHPSUnx1A4ej8T999vZsGuvreb++63A2zeLdswY63+Hg4AFucFab7ElDBpkd2f7H48vvhh4Trry\nysAvB21pwfSIC5+KSPw69FCru2jy5HTGjKnm118d7LWXJ+hi4fPVV9EPEM/IUMAVSp8+4btmq6qs\nYqrQuJmLGzY46N7dg8MBd9yRFhAwH3ecfeVfurSU999P5owzqmsX6l2woIzvv3cyeXJg+iTWMyjb\nmrp/Q253dKVRTjrJDr7PP98Kdr77roQff3SGHZvUp487ote45ZZKevd2h53McsopLjZvLg4I3mbP\nrmDdukr697fOGS0RcP32m6N2oH6kzj67mieeaFuzopXhEmljtm51cOSR7bnwQvuboscD8+dbP+fm\nutl338iCp3Hj7C6qtpLWb0njxzeuCwrg/feTOOaY9uTlZVFZGZid9P9cAA47zKqhdcABHgYMqOHI\nI10MGuTipJMC0zEffdRAUScJUjfgKo4yXq2utgONW26xPrdOneCYY0IHW489Vk7XrpH9fV53XRXD\nhtldkjk5wb8zVKasZ0/790fzfrZscYQtlFyfI45oePxg3VnCU6a0rWALFHCJJLy6NZl8ZQD8B54u\nWZLMeedZP0dT2uGaa+xaNcpwRef995OYP9++2rmjnKNwwQV2hLtgQeBVf9Kk8DWEFi4sZ8kSqzhk\n3QxK797NN9trd+EbNO/z73+nUF0Na9ZEf/m0KsuHNmdOORdfXMU559Tfhea/+LL/OMwffyzmiy+i\nD6gjzTwVF8Phh7fnvPPq/+b1zTdOhg7NZONGB6WlsHmz/fuHDw9fW6PuLOE99ohotxKKAi6RBHf7\n7YFZlPPPt0+IK1ZY/RI//2z/qX//feT9If7fjiNbc1F85swJTC1EU4H+l18CL4LXX283fseOnqhm\ni778shV8+QZQS3TqtrXDYU0+GTKkXb21tTweKPNbmW7KlIradQBDOe20Gh5+uLLBrsR//csae9e7\nd2D2slOnwLU9G/LFF1ZGKZKAq7ISJkywzjMrV9a/g0OHtuObb5I4+uj27LdfFv362W/62WcrWqXg\naLxQwCWS4PwLBNZ15pmZvP9+EvfdZ89yOuigyEf9+nenpKbqgh2NJUsCA64ePbK44Ybws83y8x30\n69eO115L5tprQ0e3GRke5s+Pbn3ZE0908cYbZaxZ07jCrru7uhMe0tLswrOrVoUOPiZMSCMvL4sN\nG+xL7KhRTayc6tWli4f164t5992mrTPsC/4a6iJ0u2HffbMCSlts2xb9uK8lS6zs2113VTJyZBXX\nXlvJJ59Y284+O7BtJk9ue92JoEHzIm2ef9cUwJtvRn6i9s9wRTNrSkJ78cVUxo6tDlkDrU8f6wro\nvz5iXU89Vc7hh0ffLdi/v0pANFbdgOvVV+3LZqiZu7t2wdy5VkA2ZIiVcrrkkubL6qSnN089vPbt\nrX33z3C5XNb6jv4LoH/4YXBQOXNmKg88EFyC5NNPw2e/jjjCPm6nT7efu3p1SW07du7sZscOJ4MH\nt83jVRkukQRW5XceHzky+KTerl3wBSE7O/Lf79+9EW7Go0THNCM/7d5zT+A3fd+yTNJy6gZcX3xh\n/yGUlgZneg48MCto2377NS47PGGCHZjcfXcFU6dWNFvx4bQ0cDg8lPtVB5k2zVoA3X9h6xdeCP6m\n5StN4s/jgb/+Nfz4rnAFgvPy7C7yDz8sY86ccvr2bZvHuQIukQS2bJkVEeXkuJk4MTjgqntB8NXj\naYxoC6XurvwHNTfVySfbA6gXLy6trdskLae+Gmq//uqo97ZPXl7jAohbbqnil1+K2bChmKuvrubK\nK5unWxKsACgtDaqq7H1+/HHrj3zJEiuorK4m5OLXoTz9dNNT4Hl5Hk47re3U3apLAZdIAvMVCSwo\ncNKxo31l6N499An+nnsaXy0+1JRzscydW0bv3i6+/LKktqilT7duge22a1fgRfnHH51BA+wBTj21\nOiDAOvpotX9rqG+NzeLiwM/SF6jUVd9g+YZkZcWuJEtamjUg3v+1wO5m9K3DCTB2bBV33GE9eNiw\n4MDv9dcDj+Gvvirh22+tAWJ33dU2x2RFS50EIgmqpgbKy60T43XXVZKRAffeW8GSJck8+WRF7Zgg\nsKpLv/pqCkVF0b/Ozz8Xs2WLs01O024up5zi4pRTrLFxq1cHjmN59tlyTjrJnj62a5d93/btjoAK\n3D4vvVRWW0Pr8MNdZGYqs9VarKxLddAkCLBKHvz0k13ANNwsQd94qXiTmuqhstI6h6xd66Sw0Pp5\n0aJkvvwyKeBYvvnmSlJS4N5703jrrRR+/rmSAw6w39fee7uBJA46yMXzz5fX1vpToV2bAi6RBLV1\nq/3t+o47rK7C0aOrGT06+NvnU09VkJbWuJR/hw7QoYOyK5EqKrI/l44dPfTt62b+/DL+9rfMoPuH\nDw9OXRx/fA1Dhtjdku+807TZaNJ04bJcX3yRzMCByaxfX0xVVfhCt9nZ8RlwuVywbp0T03Ryxhn2\nsZif7yQ/337cxRdXBWXZjj22Pfn5xbhc8PbbybzxhnV++eCDMk2wCUNdiiIJ6uqrI69iHs1SJNJ8\nhg2zxqMMHuziww+tKfD5+Q4KC+Gnn5ysXx94Cn7wwQpefbU84PNyOMIPOJaW0VDR36IiB199ZX9o\nt99eybp1dmZnjz3iM+D64w/r+DvuuHYcdVT4sYfnnht6XJXLBbNnp3D55fbMWp1rwlPAJZKAjj8+\ns3a21A03NH5clsTW//t/9iQF3xi7efNSMYws3nwzuINhzz2VSYxHZ55Z/0Du8nICAq6+fV0B47bi\nNcPl7733wnd4hVvz8ZZb0oJqkTXXLMq2SE0jkoDWrrVPchdeWP/MJV9xQWl5/jM7/Sc1AEybFlwE\ndc894//CvDs65BA369fbGau6EyGKihwBRU59XcLLlpXy4otlCb0OaVqaJ2A5sPfft88nzz+fqiW/\noqCASyTB1K0M3b176BPe1KkV3HVXRdhvpxJ7/uvwRbLsSp8++qzilf/n9/bbgePqXnwxhddeswYu\njR5dVdsF3KuXmz//ObGKeA4aFJjNW7Uq8Atbnz5uBgywH/PCC6oXEykFXCIJwOOBiy7K4OWXkwPW\nQvz005KwKfwrr6xm7Njmq9sjkfFfpsR/wepw47AmT64gP7+Y/PxiFZdNEF26BH7J6dHD/qBHjkzs\nv7kLLrD3/4QTaoLeK1gLpEv09OctkgDeeiuZd99NDlg38cEHKwKmZUt8mDmzggULrGxHJAHU3nvr\nM0wUBx7oqs10paXZJRVmzbKzPHW7GxONf7f2K69EF1g1Z9HftqjB04FhGD2B+4CvgH2BHaZp3msY\nRjYwDVgHHABMMk2zwPuciUAHoBOw1DTNN73bDwOuAdYDucAE0zQT++gUibHt2x0Bs4B80tJ0oY5H\nmZlW5nHlyqSg7t4nnihnzJjAz9Kla1TCWL7c7kpctqyU++9P4403Utixw04zp4VfnzzurF5dwokn\nZlJQYO9/Xl5k55X993fzyy/28/7xj/LaWbkSWiRdinsAL5mmOcM0zRuACwzD6AdMwQqmHgAWAjMA\nDMM4BhhimuZkYDwwwzAM3+JSLwB/N01zKuACLm3etyPS9jzySOgxEmedpZNbvDrgAA8XXBD8+Zx9\ndg19+gRGWP5Lq0h88y/Rsd9+HsaNa75FqVtDXp6H668PfA++mbJ1J3nUtWiRHXz+9FMxF15YQ8eO\nzb+PbUmDAZdpmit9GSovB1AKDAdWeLd9Agzz/ny6b7tpmi7gB2CwN1OW7suCeZ8zvMnvQKSNe/LJ\n4IDrjDOqSY+8DJfEkfHjAy9wlarqkbAyghPPCefiiwPHnHXsaGXvVqyof3Zzp04e+vVzMXp0lQKt\nCEU1hsswjL8C75im+aNhGLmAb55sEZBtGIYTq6twjd/Tirzbtvs93n+7iISxYYOd/cjPL+aoo9qx\naZOTxx/X2mSJ6vTTAzNfw4crU5mo6q6bmYj8Z1/27WtlX3v1anikT1KSVkGIVsQBl2EYQ7C6Cm/w\nbtoGZGEFTh2AQtM03YZh5Hu3+3QA8r3/OoTYXq/s7EySk9t+6dqcnKyGHyQBdoc2y/X7SpKTk8VX\nX0FFBXTt2rj3vju0WXOLZZstWULAmpdtxe5ynHXoEHh74cLGv/d4aLPLL0+Ki/2IVCLtK0QYcBmG\nMRwYZJrmDYZh7AV0BxYDA4BXgUHe23j/v8P7vBSgF7DMNM0iwzDKDMPINU0zHxjo95ywCgvbfgSd\nk5NFQYEW+IzG7tNm1gnlyCNdFBRYfwtpaVBQUN9zQtt92qz5xK7NrM/111/LKShoWxmu3e84sz7L\nrl3dDBhQmpB/m6tXO9i40cHRR7sbtf+tobXbrD7hAsFIZikeAbwMfGkYxgdAJvA4MAl4wDAMA+gJ\nTAQwTfNzwzA+MAzjfqxZihNM0yzy/rpLgCmGYWzAGj82pwnvSaRNK/N+1+jY0cOSJW3/i8fu6I8/\nNGC+rfjtt8Qta5mX54l4dqI0XoMBl2maqwjsIvQ3OsxzZoTZ/h0wKuK9E9mNffyx1ZX+t78ldiFF\nCc+ja5zIbiNxQ3KRNsrthnvvTWXECGsBtkQvpCjBUlOtSEvr0InsPhRwicSZhx5KZdYsu3riMceo\nMmZbs2RJGSNHVnHOOW1r/NbuaNQoq8yHb4afSDha2kckjtTUwIwZdrC1115ujjhCGa62pm9fN9On\nqwBXW3DNNVV89VUSEybo85T6KeASiRMffZTE3/6WGbBt9mwtEisSz/bZx6N6VBIRdSmKtBC3G379\nNfSstHXrHAHB1tixVSxZUsqRRyq7JSLSFijDJdICrr46nddeSwnY9u23Jey1lwe3G/r3Dyx+OXFi\nJe3bXj1MEZHdljJcIjE2cmRwsAVw2GHteemlZPbc0666Mnt2OfPmlSnYEhFpY5ThEmlmmzZZ3YO/\n/uqgpiawC/HPf67h3XftP7vrr7dXv+3fvyZonT0REWkbFHCJNLOjjgpOT/Xp4+L99+2Btbm5wbWE\nFy7UAHkRkbZKXYoizWjWrNSgbRkZnoBgC+zaPQAPPVTBBx+U4tAqLyIibZYyXCLN5N13k7j3XruG\n1ujRVey9t5tLLglemmfKlEqOOMLFkUe62G8/VRsXEWnrFHBJwnK5rFILKcHj0WPq558d7NzpYOnS\nZG65pQqnE0pK4KKL7LIO//1vKYcfXn9Jh3PP1XgtEZHdhQIuSThbtjg45BAoKLDGQX3ySSkHHuim\noMDBk0+mUFHhYNSoKrp3b97M0SuvJHPddRkB2zZudDJjRgU9e9pjslauLKFbN2WtRETEpoBLEorL\nBYcfHjgofeDAdkGP++UXJy++aA1C/+yzJDp29JCT46FLl+gCobfeSqZ7dzcVFQQFWwALFqSwYIGd\nYnv22XIFWyIiEkQBlySEL75w8scfDl5/PbL+w3ffTea775wUFDi48EK7q+/770vIzY0sIHr66RQm\nTUoP2j5/fhnz5qXwn/8E7svnn5doPJaIiISkgEvi3sqVTk4/PTCLlZcHJ51Uxf/+l8S33ybVbj/o\nIBfr1jmpqXHw5z8HZ7769GnPokWl7NzpYP78FEaNqub7752cf341PXtmMWRIDf/+dzmVlYQMtt55\np5R+/dwMHuxiypRKDj7Yyradd161gi0REQnL4fHE90WioKA4vnewGeTkZFFQUNzauxFXamrg/PMz\n6NHDzdy5waUWdu6EqqpitmxxcOyx7TjySBedO3t44okKli5NYsSIzBC/tXGOPbaGvDwP/fu7uOyy\n6oDyDfn5Dp59NoWbbrIGz8czHWfRU5tFT20WPbVZ9OK5zXJyskIW+VGGS+LSeedlsHx5Mh9/HHzf\nRRdV0bFjKgUFsPfeHjZsKAm4/5RTXKSmeqiqso75I45w8dxz5Tz8cCrPPhscvNXn5ZfLOPFEV9j7\nc3M93HJLVdj7RUREQIVPJQ6tW+dg+fLA7wKTJ1fw22/FzJ9fxsMPVzb4Oy680K599eST5ey5p4cH\nHgh83nnnVXPKKTVMmmRt79rVTU6OXcrh669L6g22REREIqUMl8SdqVPTAm536uRh7NhqnE4YPDiy\nAOiBByo57bQaBg92kWQP8WLlyhLWrnVy+OHugMHzN9xgZalKSuCLL5I4/ngXyfrrEBGRZqJLisSV\nZ55JYeFCa/bf11+XsM8+jRvC53QSMjvVrZuHbt3CB23t24d+noiISFMo4IpTFRVQXQ1Zfmsc79jh\noKYG8vISex5BaSkMH55J9+5uMjJgzJgqDj/czY03pvHCC9YYq7Q0T6ODLRERkXijgKuVud3QuzcM\nHJjGwQe7Oeus6oCq5aEsW1ZKr171LxsTayUl8PLLKQwfXsNee0UeGFVXw377We9vzRqrr8+/cKhP\n3YHwIiIiiazBgMswjDzgPuAw0zSP8W7LBqYB64ADgEmmaRZ475sIdAA6AUtN03zTu/0w4BpgPZAL\nTDBNs3Wjhjhw++1prF0La9damZ0JE4JrP9V1443pvPVWWax3LcBRR7Vj0yYnDz1UwU032fs4aVJk\n6wb6nHRSw+UaNmwoDhh3JSIikugimaU4EFhYZ9sUrGDqAe99MwAMwzgGGGKa5mRgPDDDMAxfuuYF\n4O+maU4FXMClzbD/CeO669LJzc0iNzeL8eOtQeGPP57C00+HLlNwwAEuevYMDGKOPNIaW+Q/ky4a\nHg+1+1BeHt3jN22yDhX/YMtn6NB25OZm4SvptmOHA1edYVCbNzu4++401q61Iqnbb68kP7+YrVuL\nufrqKrp3d/PPf5aTn19MZvOV0BIREYkLDQZcpmkuAOpWFxsOrPD+/AkwzPvz6b7tpmm6gB+AwYZh\n9ATSfVkw73OGN23XE0NJiRW0vPKK3W02b14qu3bB3XeHzmalpnr49NMyPvuslPz8YvLzi9m8uZjF\ni62s1pIlKURTr3bNGie5uVnk5dldld27Z/HGG8n07WsFSzfckMY33zh56aVkRo5MZ/NmB//8Z/hl\ndB54oIKffy6mSxc7+Fu+PImNGx307t2eXr2sCuxz5qRw6qmZ9OvXnscft4PLceOsWYFJSXD33ZV8\n+WUp55xTE/mbEhERSSCNHcOVix2EFQHZhmE4vdvX+D2uyLttO4FBm297m5af76BPH3uh5exsD4WF\nVjHOAw+0gx/ThJSUYtatc/LnP7djxYrSoN+VUif2+ec/Uxg7tjrocf4efDCV6dPTwt4/apS9GPOL\nL6by4ot2QPT224EvOHNmBZdcUo3HY43DSvU+dM2aUsaNS+fll1M455xMDjvMSm3t2uUgNzf0WLTP\nP9f4LBER2b00NuDaBmRhBU4dgELTNN2GYeR7t/t0APK9/zqE2N6g7OxMkpPrH9CzZQvss499+957\nre6w226j1WopjR4NTz5p3166FP78ZweHHw7ffmtv/+ILOOgggCz22w9v5qo94Zx7Lrz6Ktx1VzrL\nl6ezdGnox91zD0yfHrx9+XL47DOYODFw+8CB8MknoX9XVRWkpKQDoTNykyfDyy9bP/uva1jXAw/A\n2LHQvn349xeNnJz6JxdIMLVZ9NRm0VObRU9tFr1Ea7NowhH/tYEWAwOAV4FB3tu+7XcAGIaRAvQC\nlpmmWWQYRplhGLmmaeZjjQtbTATy88uCsjseD7Xr2U2alBY0DuqOO6z/9967nL/8peW6qVatcrJ1\nq5PVq508+aSdWfrf/0rIyfFQUACPPupk8GBrUeV+/Vz06FEGRL4m1JgxTl591Xr+u+/C+edba/tN\nm1bBo4+mctVV1XTp4uHOO+0D8fbbK2u78MAK8EaMgPJy6NHDetzrr9uvv327o3ZR5u++K2Hnzvr7\nL7t0gYULkzjzzODBV9OmWZmx7793csQRbsrLiWj8WEPieR2teKU2i57aLHpqs+ipzaIXz20WLhBs\ncPFqwzCOB0YCpwD/xBogn4k1S3ET0BO41W+W4gRgD6xZiktM01zk3X4oMA7Y4L1/YiSzFB0OPM89\nV86wYTWsWBF4Ub/++kr+8Q87sBk3rpJHH7Vvn356NbNnVzT0ElErLbVLGwBccUUVCxcms2NH4JC4\nZ58tZ/jw0AHfzz876NnTg9MZ3YHjHwyFsscebt5/v4zDD7ces3FjMRkZYR/OypVO8vI87Ltv02te\nbd3q4Npr07nssmquvDKDe+6pYMyY+rs9Gyue/9jildosemqz6KnNoqc2i148t1m4xasbDLham8NB\nRDu4bl0x7dtb3V8Affq0Jy/PzccfN718gscDs2al0q+fi332cdO/f8NdYm+8UUb//pFVLI/2wHnp\npShhxjIAACAASURBVGTmzEll1ar6u1pPPrmGefOaIZ3UCP5ZyFiI5z+2eKU2i57aLHpqs+ipzaIX\nz20WLuBKyMKnRxzhCgg2fv21mDRvYss3mHvnTgc7dyZRU9O0cVx//AG9eoVOD558cg1Ll9q/fOHC\nMgYMiP2yMBdeaGXNVq2qJ3UFPPJI82f3IhXLYEtERCTRxH3A9corZZx/vt2N+NlnJfTs6cHlsmbL\npTdQJ/TXXx3st1/kWbzZs1N4/vkU1qxJ4pFHyrnhhtBBzccfl2IYbgoLYe3aJA47zNWi9aMuvLCG\nPfawArwOftMRRo1K5403Uhg7toqcnPjOXoqIiOwu4j7gOuEEF/n5wWnDpCQiqkZeXOyAEL2SO3Y4\nqKqidlmaLVscteOefPyDrbffLuWAA9ykpVGbTQPIzqZFslqhnHJK8Os++WQF995bGdVyOyIiIhJb\nkVSaT0iGYQUj/rWmfD74IInevdtz2GHtyc3NYsSIjKBgy+eQQ1xs2VLMEUe46dAhMNiKR04nCrZE\nRETiTNxnuBprv/3cmGYSGzZYZRoOPthNaSls2+YM6KIEeOcduxnmzi2rzRyVl1vjv1qrlpeIiIi0\nDW02lLj11qraauknndQuoucMH14d0E1XXzkFERERkUi12YDr4IPrL/G1bVtx7Uy6zz6z1gA8/3yt\n5SciIiLNr82O4QLo0SN00PXKK2UBZQv693cp2BIREZGYabMZLoAlS8pYv97BUUc1WNBeREREJGba\ndMDVubOHzp01Y09ERERaV5vuUhQRERGJBwq4RERERGJMAZeIiIhIjCngEhEREYkxBVwiIiIiMaaA\nS0RERCTGFHCJiIiIxJgCLhEREZEYU8AlIiIiEmMKuERERERiTAGXiIiISIwp4BIRERGJsRZfvNow\njJOAs4FtAKZp3tPS+yAiIiLSklo0w2UYRgbwBHC9N9A61DCME1pyH0RERERaWkt3KQ4ANpimWeO9\n/QkwvIX3QURERKRFtXTAlQsU+90u8m4TERERabNaegxXPtDB73YH77awcnKyHDHdoziRk5PV2ruQ\ncNRm0VObRU9tFj21WfTUZtFLtDZr6QzXCqCbYRgp3tsDgcUtvA8iIiIiLcrh8Xha9AW9sxT/hpXZ\nqjZN894W3QERERGRFtbiAZeIiIjI7kaFT0VERERiTAGXiIiISIwp4BIRERGJMQVcIiIiIjGmgEtE\nREQkxhRwiYiIiMSYAi4RERGRGFPAJSIiIhJjCrhEREREYkwBl4iIiEiMKeASERERiTEFXCIiIiIx\npoBLREREJMYUcImIiIjEmAIuERERkRhTwCUiIiISYwq4RERERGJMAZeIiIhIjCngEhEREYkxBVwi\nIiIiMaaAS0RERCTGFHCJiIiIxJgCLhEREZEYU8AlIiIiEmMKuERERERiTAGXiIiISIwp4BIRERGJ\nMQVcIiIiIjGmgEtEREQkxpKb8mTDMA4CLgTKgeOBu4BfgGnAOuAAYJJpmgXex08EOgCdgKWmab7Z\nlNcXERERSQQOj8fTqCcahuEE3jBN83Tv7TzABdwLvGea5quGYZwOnGea5kjDMI4BJpumebphGEnA\nD8CRpmkWN8s7EREREYlTTelSPBpwGIZxnWEYtwJnmKa5HRgOrPA+5hNgmPfn033bTdN0YQVcg5vw\n+iIiIiIJoSldit2B/sD5pmmWGIYx1zCMaiAH8GWtioBsbzYsF1jj9/wi7zYRERGRNq0pAVcRsNY0\nzRLv7eXAECAfyPLe3wEoNE3TbRiGb7tPB+9j61VT4/IkJyc1YTdFREREWowj1MamBFyfA50Nw3CY\npunByniZWAPoBwCvAoOAxd7HLwbuADAMIwXoBSxr6EUKC8uasIuJIScni4ICDWWLhtosemqz6KnN\noqc2i57aLHrx3GY5OVkhtzc64DJNs9AwjFuAfxiGUQB0Ae4GMoFphmEYQE9govfxnxuG8YFhGPdj\nzVKcYJpmUWNfX0RERCRRNKkshGmaC4GFdTZXAqPDPH5GU16vMUpKwOmEzMyWfmURERERS5MCrkTQ\ns6eV2tu2rRhHyF5VERERkdhq05Xmv/7afnv//a8G3ouIiEjraNMB1//9X2rtz1demdGKeyIiIiK7\nszYdcB15pKv2544dPYwYkcHy5cp0iYiISMtq0wHX5MnptT8XFDh5551kzj5bo+dFRESkZbXpgCsl\nJfQ6kdXVLbwjIiIisltr0wHXVVeFjqy2btV0RRERkXhx1VUj8XhCJ0maQ3GxVSR1ypS7ASgqKqKs\nrIyamhpmz36S33/fSlGRVRp01qyZPPXUP5k79znuvHMShYV/NMs+tOmyEL7P7uSTa1i61H6rv/7q\npFs3V5hniYiI7B7uuiuNN99s3lDgjDNquOuuyqie89RTzzfrPtT1008mH330Plu2bOb552fjcrkY\nNGgwb7zxOvn5v1NdXY3LVcNVV40lIyOTUaPGADBv3hzmzJnNDTdMbPI+7BYBV/fu7oDtq1c7GThQ\nAZeIiEhL27RpIy+88BwHHHAgP/5o0qtXb1555UVmzXqSPffckyVLFvHpp8s56CCDX375mT/+2MEN\nN0xkzpxn2Lp1K0cf/Sd+/HENf/rTQHbu3MmPP5oYRi+uvNKquT5p0k307n0IBQXb6NPnMIYOPZVu\n3XrQpUsOq1atpKSkmAEDBpGXtyddu3bl559Ndu7cycCBx5GSklIbbAG43R4yMpqnysFuEXB16hSY\nply+PJkxYzSQS0REdm933VUZdTaqqT777FNSU1M5++zz2L69gJSUFJYt+xCAoqJdPPHELF57bTHJ\nyck89dQ/6d69Bz17HsDVV4/juutGc9VVV5OeDoMGDWLx4ndJTU3j3HPPqA24hg07g0GDjsftdnPx\nxecydOip/P77Vk477XR+/XUTV189jo8//ogdO7YzYMBAysrKOO20M/j5ZxO3243TaY22Ki4uZuXK\nz7nvvgeb5X3vFgHX4MEupk+3t//3v8mUlED79q2zXyIiIrurv/zlLF544TnGjh1F9+49uPbaG2rH\nb23e/BvZ2Z1JTrbCk7333of8/G21z91rr70ByMrKIju7M2lpVjUCp9Mq+eRyuVi/fh0//riW1NRU\ndu3aBUCfPn0BuOCCS3A4HBx//JDa3zl06GnsscceDBo0uHZbaWkJjzzyILfddidZWaEXo45Wmx40\n7/b2JLZr5+Gqq6oYO7aq9r6vvlI9LhERkZa2Zs33jBhxGU8++RzZ2dm8/fbi2vv22acrhYV/UO0t\nJ7Bly+ba+zweT52B9cE/r1ixnJUrP+eKK/4fl1xyGWlpaQGv3bPn/kH7s88+XUlNtQul79y5k5kz\nH+Dqq69nzz335KOP3m/Cu7XtFhkupxPuv99Kme67r5vbbktn7Vonhx7qIju7FXdQRERkN1NUtItH\nH53J3nvvw86dO9lrr33Ytu13Fi58jdGjr2H06Gu4885J9O59CH/88Qd5eXkALFq0kG3bfufrr7+i\ntLSQ0tJSPv74QzweKC0tZdGihQwceDz//vdLPPLIdHJycqioqOCtt95k2LAzIt6/G/9/e/cdJ2V5\n7n/888zM9kJdmiiI6A1KEQ0EFAUxYsOS2P0ZjV2jJh5rYokNe/B4NCeeRI31qDFWsGBUQBGRg6hI\nvS0oKgosRVl22TLzPL8/7lmWtrCzu7M7M/t9v177YufZZ2buuZhyzXW3yy7G931uvvk6giCgoKCA\nUaPGNPlxe8mchtkcSkvLGt3Aq6/O4ZFHsnnnnXL693flro8/DnHooQUbz3n77XIGDvTru4kWUVJS\nRGlpWau2Id0oZolTzBKnmCVOMUucYra5xYsX0q/fngA8+uhD9OjRk7FjD9vsnFSOWUlJ0TbXnmoT\nFS5vk4fer9/mydXBBxewcmVq/qeJiIi0NW++OZkZM6aTnZ3Njz/+yOmnn9XaTWoWbSLhCm0yUi0v\nD3r29PnuO3ewb18tDyEiIpIqLrnkstZuQlK0iUHz3hbFvUGD6pKsL77Q4HkRERFJroxOuGqFQpsP\nA+vUafPLn3zSJsIgIiIirSSjM436KlzHHx/d7PJ1120+bVRERESkOWV0wlXfBMxNuxRh64qXiIiI\nSHPK6ITL911pK7TFoywogBtvrOQvf9lAUVHAkiUZHQYRERFpZW1iluKWXYoAv/2tW8X2kUd85s4N\nUVMDWVkt2DgRERFpMzK6tLOtZSG2tOeeMaJRj4ULMzoUIiIi0oqaVOEyxswENgAeELXWHmKM6QDc\nASwB+gLXWGtL4+dfARQD7YE3rbWTmnL/O1LfoPlNDR7s88QTcM892Tz2WGUymyMiIiJtVFO7FF+3\n1t68xbHbcMnUc8aYccAE4HRjzDBgtLV2nDEmDCwyxkyz1iZtmfeGVLgGDnQD6F9/PYtYrJKwluUS\nERGRZtbUfrRBxpgrjTE3GGOOiB87EpgZ/30GUHt8XO1xa20MWASMauL9b9f2xnDVGjKkbqufDz5Q\ntiUiIiLNr6kJ1x3W2ruBW4BrjDEHACVAbdVqHdDBGBMCumxyvPZvXZp4/9vVkIQL4JprqgD45S/z\nqa5OZotERESkLWpSl6K19sP4v74xZjpwELASKMIlVMXA2vjfa4/XKo6fu10dOuQTiTSu8pSd7f4t\nKSmkpKT+804/HW67zf2+eHERBx/cqLtrkpKSoh2fJJtRzBKnmCVOMUucYpY4xSxx6RazRidcxhgD\n7G+t/Uf80O7AC8CrwAjgOWBk/DLxf6+PXzcL6Ae8u6P7Wbu2orFNZMOGXCCL1avXEw7Xv7hpx45w\nyCF5vPlmhJdfrmLQoJYtc5WUFFFamrShbBlJMUucYpY4xSxxilniFLPEpXLM6ksEm1LhWgccYYzp\nDrQDvrHWPmWMeR24I56Q9QGuALDWzjLGTDXG3IqbpXi5tXZdE+5/hxoyaL7Wf//3BvbYo4hPPtE4\nLhEREWlejU64rLU/AMdv4/ha4Px6rjOhsffXGA1ZFqJW+/bQv3+M2bPDVFfXdUeKiIiINFVGr/ZZ\nV+Fq2F6Jw4fHqKz0mD8/o8MiIiIiLSyjM4tEKlwAw4a5NbmmT8/oHY9ERESkhWV0wlVT4zKthu6R\nePDBUbKzA156SQmXiIiINJ+MTrhq19TKyWnY+e3bw4gRMRYsCFNa2sCymIiIiMgOZHTCVVXlxm9F\nEihYDR/uuhXnzMno0IiIiEgLyuisYsWKEL6fWKVq6FCXcL3/vroVRUREpHlkdMK1dGniD2/YsBj5\n+QGvvRYhFktCo0RERKTNURlnC7m5bvD8pElZfPFFCGP8HV9JREQkQwQBLFgQYuVKj1AIunYN6NbN\np317N+t/3Tr48UePSMRdXrQoxD//mcWaNR5dugTk5QW0axfQqVPALrsE7Lqrz267+eTmtvYja10Z\nn3B16pR4wrTnnj6TJsEpp+Tx0UflSWiViIhIagkCePjhLB5/PIvFi7fedSUnJ6BDh4AVKzyCILHh\nOjk5Af37+/Tp4xMKuR1gunXzKS6GggL3t6KiAN+HSAT69vUbPOEtXWRswrV2rft39erEuxXPOqua\nO+/M4bvvMrrHVUREBIAVKzwuuCCXGTNcWjBgQIyjj44Sjbq/uZ8QpaUeI0bE6NkzoKYGKith+fIQ\nhx8eZdSoKLm5EItBRQWsWhVi6VKPJUtCfPxxmIULQw3ePi87O2C33Xy6dXPJ2F57xRgyJMZuuwUN\nXlsz1WRswvXpp43fE7FDBzjqqBomTcpi4cIQe+6pbkUREclM33zjcdhh+axa5YoM9923gZNOijZD\nYrP5Z2c0CkuXemRnu6Rs+fIQ69e77slFi0Js2OARDsOGDTBvXpjPPguxaJHH1Kl1t1FY6Loo99gD\n2rfPoXdvn65dAzp3rkvQWjIhC4KGL66esQlXXp7bzuf886sbdf1DDnHjuKZMCSvhEhGRVlFZCd9/\n77FgQZgVK1xCkp8fEATQpUvATjsF7LSTT2Fh427/s89CjBxZALhCw623VtGtW8O2w0tUJAK77VZ3\n271773hmWlkZzJ8fZsGCEHPmuH+/+CLEvHkAW296nJ8f0KePz+DBMfbZx40d69rVp2fPYJtdlEEA\nq1d7fP21R7t20LWr6+bcnunTwzzwQDZz54ZYtcqjuNhdLxr1KC+H5cvrefw7fLRpqnY5iPz8xj1x\nxoxxT4Q33ohw8cU1zdYuERGRhnj66Qi//31eg87Nzw/o2DFgwIAYHTsG9O3rM3CgT7t2AcXFAd27\nB+RtcVOTJkU4+2x38KijanjoocqU664rKnILko8YEeOcc9xncRBALFbEp5+Ws3RpiG+/dZWyJUtC\nfPml+5k/P8z//u/mt9W5s0/nzgHr13v4vqtMbdgAa9ZsPnyosNAlsd26uQkAHTq4iQKzZ7ues5Ur\n3fm5uQH77ONTVgbffhvC96FXr/oLNBmbcNVq7JOnS5eA/v1jzJoVYc0a6NixedslIiKZ7dtvPRYv\nDhEOQ0WFR6dObubeihUeFRXuWH5+wIABUFXl8cMPIXr1cl1kWVnw+uvuI7p9+4DDD4/Su7dPr14+\nZWUeNTWwbp3HsmUe338f4vvvPZYvDzF5cv172XXs6JKI4mJ3+7X7Bh90UJQHHki9ZKs+ngfdu0Mk\n4rPPPlsnONGomzk5d26Yb791ca2N09KlIWpq3MzLcNjtMNOvX5TddvMJAtfNuWyZu461mwekfXs3\n+3KPPWJcdVU148ZFCcVztSBwP+5y0TbbnbEJV6IbV2/LuHFRFi0KM3FiFr/5japcIiKybZ99FuKN\nNyLMnh3im2/ckgq1Y6Iapq5P0PPcbMA1a0Lk5ARYu75Bn2VBAKtWefz0EyxaFGbePNflVVHhUVrq\nEo7aalAQeOTlBZx5Zg033liV+ANOYZEIDBzoKnxbctUxGrQDzfr1UFnpUVYG5eUee+7pb0ywtuR5\nO843Mj7hqi84DXHCCTXcfXcOkydHlHCJiMg2vfdemF/9Kn/j5exs1303cmSUPff06dTJbTG3Zo3H\njz+6brJwGIqK3PFVq3L4/vsali/36Nkz4IcfXIXF9wOuv76qwYUDz4OSkoCSEujbN8pRR237PN+H\nmpqG7zOcSTyvYckWQGGh617s3Bmg6ePalHBtR+/ebjbEBx+E2bCBrfq/RUSkbfvkkxAnnug+HEaN\ninLPPZX07JnYTLmSkhxKSyuT1MKthUJtM9lqbRm70FRzJFwAY8dGqajwmDWr8ctMiIhIZgkCuP/+\nbMaOLSAa9bj99kqeeWYDO++cvutESXIp4dqBgw+OAvD22xlbDBQRkQZ65pkI556bS/fuhdxyiysT\njR0b5eyzawjre7lsR8YmXEG8u7Wp3zSGDo3Rrl3A889HiEab3i4REUlPGzbA736Xx8svZ+H7Hnvu\nGWP69HKefHJDazdN0kDGJlx1Fa6mDXQrKIBjj61h1aoQL76oKpeINL8gYOMWKh9/HOKTT0IsWeJt\nfB+T1PDnP7uFNg8/vAZry5g2rQJj9J8kDZOxGURzdSmCWwT1scfg0ktzOeGE9U2/QRFp83wfnngi\nixkzwrz00rbXTsrPD6io8OjY0WfXXd3WJbvv7jN8eIx99omRVf+SS5IEkye7j8yrrqqmQ4dWboyk\nnSYnXMaYXGAW8Ia19ipjTAfgDmAJ0Be4xlpbGj/3CqAYaA+8aa2d1NT7r0/tSvPNkXAddpjrS6yp\ncRt4du2anG0PRKTtuPvubCZM2Hyq2BFH1FBc7BZYXLXKLZpZWuo2DV63LmDOnLpBQgUFASNHxhg5\nMkqPHgHr1nl07+6z664++fnofaqZPf98hM8/DzN0aIy99lJVSxLXHBWu8cBHm1y+DZdMPWeMGQdM\nAE43xgwDRltrxxljwsAiY8w0a21ZM7RhK7VjuJoj4fI8uPXWSq69NpcXX4xwwQVak0tEGq+qio3J\n1ssvV7DvvjGyt94WbjPRqNtkeMGCMO+9F+bddyO88Yb72ZaePX322y/GgQdG6dvXZ489Gr/fnsA1\n1+QCcNZZjdufV6RJCZcx5jTgPWAwUBA/fCQuCQOYATwa/30cMBPAWhszxiwCRgGvNKUN9WnOLkWA\no4+Ocu21rqSshEtEmuLf/3ZvvX37uj3iGiISgT59Avr0iXLUUVGgiu++85gxI8zKlSE6d/b5+usQ\nX30VYsMGj9mzQzz7bBbPPuv6HUOhgL32quuOHDDAJWFawmDH3nsvzNq1LlDHHafZU9I4jU64jDH9\ngX7W2uuMMYM3+VMXoLZqtQ7oYIwJxY8v3OS8dfFjSdFcsxRrde0aMGJElPffj7B0qUevXirXi0ji\nNmxw6zcB3Hxz07ZU6dkz4KSTtp0A+D4sWBDigw/CfP11iHnzQnz8cZh58+q6Jbt08Rk9Osahh0Y5\n8MAo7do1qTkZ65FHXNJ6440ttzipZJ6mVLh+CVQaY64GRgJZxpjfAytwOzeuw43XWmut9Y0xK9l8\nR8diYOWO7qRDh3wikcQXN6ktnbdrl0tJSW7C19+Wc86BmTPhjTcKufbaZrnJjUpKtr3ZpdRPMUuc\nYpa45ozZqlUwfDj88AP06AGHH55P+/bNdvNb6doVxoypu1xZCbNnw0cfwaxZMGVKiGefdZWwcBj2\n3x8OOQRGj4Zhw9hhN2d9Mu15tmiR24rnT3/KxfOa5/NkS5kWs5aQbjFrdMJlrb2t9vf4wPkCa+1/\nGWMMMAJ4DpeIvRo/7VXg+vj5WUA/4N0d3c/atRWNat+PP0aAPMrLKyktbZ4uwFGjICenkL/9LeDM\nM8ubbYZQSUkRpaVJGcqWsRSzxClmiWuumJWXu+Rq8WL35XHAgBgTJ1ZQUwOlpU2++YT06+d+Tj3V\nVcHmzXObLk+dGmH69BDvvuu6BcLhgD328Nl//xg/+1mMAw6IUVKy48p+pj3PYjFYurSQwYN9Vq1q\n3OfRjmRazFpCKsesvkSwOWYp/go4AMg2xpwEXAPcGU+8+gBXAFhrZxljphpjbsXNUrzcWruuqfdf\nn+YewwVQXAxHHhnlhReyuOGGHG67LbN2WBeR5vf3v2dx3XV1VZGjj67hL3+pJDc5hZKEhEIweLDP\n4MHVXHVVNWvWwPvvR5gxI8ycOWGsDbFoUZiHHnLn77yzz4gRMYYNizF0aAxj/GZ9j01Fy5d71NR4\n7LKLZiZK0zQ54bLWvgC8sMXh8+s5d0JT76+hYvFxqM39ZnDRRdW88EIWDz2UzS23VGkrBxHZptWr\nPfr3r5sWePjhNdx7b2VKr9/UsSOMGxdl3Dg3LqyyEj79NMSsWS4J++STzQfiZ2UF9Ovn06uXS8QO\nPDBG586t+Qia3xdfuA+RPn2UcEnTZOzCp2+95R7axx+H+H//r/lud+BAn8MPr+H117OYPj3M6NEN\nm2EkIm3LH/5Qt8bWVVdVccUV6becQG4uDBvmM2xYNZdc4noOrA0xe3aYWbNcBeyzz0LMmxfmlVdc\nEtapEwwcmEffvj5DhsTYd98Yu+6avhs6z5zpvlXvtpsSLmmajE24unVzYw322KP5XyQXXugSruef\nz1LCJSJb+eyzEC+/7BIQa8tSuqqViFAI+vf36d/f5/TT3dhY34fvvvN4770w06dHmDMni2nTIkyb\nVne9rl19evf2Wb/e46uvQsRikJ/vFm9t3z7gZz+LMXiwzz77tGw3ZRBsfyb7p5+GuOcelzgPH673\nemmajE24dtrJJVo9ezb/8g3DhsXYZRefV16JcNttUJReEyVEJMkee8wlW0cfXZMxyVZ9QiHYZZeA\nU0+NcuqpUUpKsliypIxFi0LMnRvm//7P/cyaVfdxM2hQjOpqKC/3+PLLEPPn143N6NTJZ9iwGP36\nuXXCdt/dp18/v9EzJjcVBPD++2F++MFj2rQIL74YITsbevTw6d49oHPngGjUVfHWr/dYtsxlfuef\nX83OO2spIGmajE24mmvz6m0JheC002q47bYcHnkkm9/9Lv26CkQkOWIxePxxl3Bdf33bnFhTVFTb\nFelz7rmuErZmDaxd69Gnz+bdi9XVbr2wTz913ZQzZ4Z5/fUsXn+97pzc3ID+/X2qqqCoyM2eHDTI\ndVn26BHQsaO7zU8+CVFV5ZGbG9C379Yr6597bi4TJ9ZNL+/Y0adz54CVK0N8/nldowoL3W327u2z\n335R/vCHtvn/KM2rDSRcybn9M8+s5j//M5vbb8/mwgurtYmsiAAwf7770B8wIKYFkjfRsSN07Lh1\nPLKzYcgQnyFDfM44o4YgcDMDv/gihLXu5//+L8z8+aGNk6E2rZaBG7xfXBywenXdG344HLD77j7d\nugV07RrQqVOwMdkaNSrKWWfVMHp0lLw8d/6GDbBihUcoBDvtFGhClDS7DE64mm/z6m1p1w6OOirK\ns89m0atXIf/+dwUDBmhQpUhbd/XVbr2H885T5bsxPA+6dw/o3t2t/VUrCNxPdTV8+WWIDz8Ms3hx\niOXLPZYvd5t8DxkSZc89Y/z4o8fChWE++yzE4sWbD9I688xq7rxz64pVXh707q0EWZInYxOu5ty8\nuj4XX1zNs89mEY16jBlTwP33b6h3mw0RyXxz54b46CNXGnH7HUpz8Tz3k5sLe+3ls9deDfuCW1EB\nK1d6rFzpsWaNx8iRGvwurSNjl6yr7VJM5lTkfv187rtvw8bLN9yQs52zRSTTjR/v3gMuvbSKgoJW\nbowAbjZk794Bw4b5HHZYbKtxXSItJeMTrmRPLz755CjjxtUOCnVr0ohI2zN7doh33nGdBldeqe5E\nEdlcxmYHLZVwAfz975Xcf7+rdD34oEbPi7RFN9zgxm49+OAGTaIRka2kRcIVNGIcY0t0KdaKROD4\n46P06OHzr39lUVqapksqi0ijrFjhMWdOiMGDYxxzjMZuicjWUj7hevLJLIwpZNGixJraEoPmNxUO\nu30WKyo8nnhCX29F2pKnn84iCDxOOKGmtZsiIikq5ROu8eOz+fFHjxdfTGxCZUsnXAAnn1xDpkYE\nfAAAIABJREFU+/YBDzyQTUVFy92viLSul15y70+HH67qlohsW8onXBs2uO656urEuulaskuxVlGR\nW+Plp588nnpKVS6RtqCiwu2dmJMTaPsXEalXyidckXhhK5rgF8dkbu2zPeecU0N+fsCf/5zNunUt\netci0gr+9rdsolGPs85Sd6KI1C/lE66sLJcw1ST4XtaSsxQ3VVIScMkl1axZE9q4n5qIZK477nC7\nKg8bpgU1RaR+KZ9w1e5nlXiFK7lb+2zPb35TQ2FhwP3357BqlWYsimSqf/4zQhC41/iRR2r8lojU\nL+W39qldzyYabdwYrtZIuDp1Crj88ipuuimXO+7I5s9/1k7zIunE92Hq1DDWwowZeZSWeixZEqKw\nMKBdu4BYDL77LkRFhXtfevJJzZIRke1L+YSrdgxXol2KrTFLcVPnnVfDM89k8fjj2Zx4Yg3Dhmlj\na5FUt2qVx3HH5bFoUXiTo+5NaLfdfCoq4NtvQwQB5OS4AfPXXVfF2LHqThSR7Uv5hKu2wtXYMVwt\nOUtxU1lZcNddVRxzTD6//30e06aVk5MDb78d5pRT8gH4/vuyjQmliLSuDz8McfbZefzwg/uW1rmz\nz4MPhthll/X06BFsHN4gItIYKT+GKy/PlaoqK9OnS7HWiBExTjutmi+/DHHPPW5g7fvv171rX3BB\nLtXNvOVaTQ28+GKEpUs1dkykoWbNCnPEEQX88EOIU0+tZtmyMhYuLOfYY2HnnZVsiUjTpXzC9cMP\nLnFIdCHRVEi4AG66qYqdd/a5//5s5s0LUVJSt0zFxIlZ/Pa3uY3aughg9WqPLl2KOOaYPMrL3bH3\n3gtz/vl5DB1aSJcuRXTpUsTMmfq0ENmee+91X4j6949x771V2gtRRJpdyidcq1e7JtYugNpQqZJw\nFRXB3XdXEo16/O53uZSVucfxj39sYMiQGBMnZjFuXOP2izzsMNc1OXNmhF13LcKYQl58cetPimOO\nyefCC3P58ccmPRSRjLRuHXzwQZhu3XzeeUeD30UkORo9gsgY4wGTgA+AHGA34EwgH7gDWAL0Ba6x\n1pbGr3MFUAy0B9601k5q6P01vsLV+is/jxnjuhaffDKbBQtctaljx4C//W0Dw4YV8tpr0LVrEZ4X\nUFQEM2eWb1YJ25ZoFJYu3TybXLvW45lnXML1hz9Ucdll1UyZEubyy3N5/vks/v3vCM8/X8Hee9cN\n4H/99Qjr1sGJJ0ZbbbybSGv68MMw5eUep52mhUtFJHmaWv9531o73lp7PS7ROg64DZdM3Qm8DEwA\nMMYMA0Zba/8E/AcwwRhT1NA7qqpKLBto7VmKW7rppip22qku0cnNDejdO+Cll+oyySDwWLfOY/jw\nAr7/vv7He/nlOfTo4ULXrZvPihVl3HNP5WbnnHii+/AYMybG1KnlHHVUDWVlHscck8+UKXVdjGec\nkccll+Rx553Zje7aFEllFRXw6KNZPPlkFv/6V4Snn45w113Z3HxzNscdl8fJJ7tK8YABmmkoIsnT\n6AqXtTbAJVcYYyLATsBiXHVrfPy0GcCj8d/HATPj140ZYxYBo4BXGnJ/jd3aJ1WqNkVFcM89lZx0\nkntzz3ZDRthvvxi+D3feWcl//Vc2y5eHKCvzOPjgfCZPrqBXr62zoCeeyN74+513VuF5cNppNZx2\nWg3l5W66+qazH9u3h4cfruT116Oce24up5ySx0UXVXPVVXUj9u+5J4f16z1uvrkqZZJUkaZascJj\n770LiMW2/0bQs6fPEUdo4VIRSZ4mL0pgjBmLq1i9Yq39yBjTBSiL/3kd0MEYEwK6AAs3ueq6+LEG\n8RNcxqo1V5qvz0EHxbj22ipeeCHCrrvWPSDPg7PPruHss2sIArjhhhz+53+yGTq0kA8+WE+fPnVJ\nVzQK4XBALObx0Ufr6dlz84SsoKD++z/88CgTJ1ZwwQV5/OUvOUyc6LofhwyJUVEBf/97Nt984/HX\nv1ZSWNi8j10k2ebMCfHUU1nU1Hh4HqxdC1OmRIjFPEIht+VWz54B33/v0b59QNeuAfvtF6OkRLMQ\nRST5mpxwWWv/DfzbGPOYMeZCYAVQhEuoioG11lrfGLMyfrxWMbCyoffj+yFKShrcA7mxgtS5cyEl\nJQ2+WtKNH+9+Ng8Fmz22Bx6An36Cp5+GI44oZNo0GDjQ/W3pUojF4NRTYciQxLOiQw+FTz+FSy+F\nf/zDZaPdu4d5/HE44QSYPDmLPn2y+J//gfPOS50K4bYk8nwQJ91iFo3CfffBsmXuNbHPPtC1K/Tv\nD7m58NVX8NprsHAhTJ687dsYNw6eftqjsDCnUW1It5ilAsUscYpZ4tItZk0ZNN8f2NVa+1r80FfA\nrsCrwAjgOWBk/DLxf6+PXzcL6Ae829D7q6ryKS0tb3D7KipygSzWrl1PQUFqD04qKSmitLRss2P/\n9V+w555ZXH99LoMGwSuvlDNsmM+11+YA2XTsWEVpaeMX8brjDjAmi6uvzmXYsEp8v4bHH4frrsvh\nsceyueACePbZKKNHRznjjBry8pr4IJvZtmIm25dOMQsCmD07xO235zBjRt3b1MMP13+dwsKAQw+N\nctll1YTDAdXVHn36+GRnw4YN7idR6RSzVKGYJU4xS1wqx6y+RLApFa4q4CxjzN5ANi6B+h1QA9xh\njDFAH+AKAGvtLGPMVGPMrbhZipdba9c19M52NAZjS6k2aL4xzjuvhlAIrr02l3HjCnjhhQr+939d\n6W7EiKYP8D3zzBqOP75mY/dhTg7cfXcVv/51DX/8Yy5TpkSYMiXCzTfncPrpNZx3XvVm3ZsizS0I\nYPLkCGecUZfh9+8f49e/rmHNGo+uXQPWrvWYPz9EdbWbTBOLwRVXVDN0aGyLrkE9V0UkdTRl0PwS\n4Ph6/nx+PdeZ0Nj7S3TQfCYkXJ4H557rPmgmTMjhzDPrPoQOPrh5ZlQVbSMRHzTI55VXKvjwwxBH\nHllANOrxj39k88QTWVx5ZTUXXlhNTgN6Z4IgtbskJXXMnRvilltyeO+98MbxlwC3317JmWfWpPXr\nWEQE0mAvxVqxBPOLVJul2BRXX11Nnz4+F13kEq6xY6NJ/wDyPBg61GflyjIqK+G11yJcd10Ot93m\nfq69topLLqneZjuWL3czw3zf44wzqrnssmq6d1e1IVMFgftCVFrqUVkJ7dsHFBfXzZQNAvj88xBf\nf+2Rl+e69srKPAoKAubPDzNjRnizbsNevXx+/esaLrywWiu+i0jGSJuEq7GbV2fKN+MTToiSlbWB\n8eNzOPLIll2gMTcXfvWrKCNHxvjjH3OYNCmLW2/N4a23wkyYUMUee2w+hfTGG3M2VikeeyybZ57J\n4vTTazjqqCg/+1lMG3ZniIkTIzz2WBZz5oSpqNj6m023bj7t2wesXOmxZs2OX4iXXFLFH/9YreeH\niGSktHlrq6nx8P2GJ1CZlnABHHtslGOPbb21grp0CXj44UpWrariqqtyeOWVLMaMCXPppdX88pc1\n9O4dsGqVxwsvuLLEo49uYO1ajzvvzObBB90PwH77RTn//BoOPTT5lTpJjokTI5xzzuYzKQ4+OEpW\nlhusvmEDLFsW4ttvQxQXBxxySJRevXyKigJ++slj/XqPnj19fvrJo0ePgFGjogwalODaLyIiaSRt\nEi5w4zyGDGnYm3Iqbe2TaTp3DvjHP9xCqldfncNdd7mfTY0cGd24kOSvflXDG2+4AfiTJkV4/333\ns8ceMa65pprDD9e2QukiFoOlS72NydbFF7stpLRum4jI9qVVfSGRpQkyscKVag4/PMp775Xzm99s\nvTzFHXdUbfw9L89V5+67r5IlS9YzdWo5v/xlDZ99FuY3v8lj7Nh8Jk8Oa2uhFLdihce4cfkMH+6y\nq8GDY/zpT0q2REQaIq3SkaqqHZ9TKwhSb6X5TFRcDHfdVcXKlWVYW8bMmeuZO3f9VuO6anke7LWX\nz9/+Vsn06eUcc0wNc+eGOf30fMaNy2faNCVeqSYahWuvzWHw4ALmzHHrLpx3XjX/+leCO8qLiLRh\naZWObGtgbn0yaZZiuujQAXbbLWjwjERjfB58sJK33y7nsMNqmD07zIkn5tO1axHnnJPLtGlhqhu/\ntqs0k2efjfDgg9n4vsdll1XxzTdljB9fRfv2rd0yEZH0kVZjuFasSDzhUoUr9Q0c6PP445XMm1fN\nTTfl8O67ESZOzGLixCyKiwN+8YsoBx0U5aCDYnTpovJXS5s1y71NvP56Ofvuq4HtIiKNkVYJ18qV\nSrgy2cCBPs89t4HycjcLbt68MJMmRXjhhayNMx/z8wPGjo1y0kmw114e3bopAUu2OXNCFBQE7L23\nki0RkcZKq4SrslIJV1tQUACnnBLllFOijB9fxdy5IWbMCPPWWxE++CDMSy9l8dJLAIV06uSTm+vG\n9w0a5LP33jFGj47xs5+5bV7Updw0ixaF+OyzMAccEN1i2xwREUlEmiVcDT9XCVdmCIVgyBCfIUN8\nLr64hiCABQtCvPNOATNnRpk9O8zq1W5189q9H++5ByKRgGjUo1cvnwMPjDJ6dIz99ovRqZMqYol4\n5BFXWRw1qnm2khIRaasyNuHKhL0UZWueBwMG+Bx0EJSWbsD33dpQWVmwbJnHggUh3ngjwjvvRPjm\nG4/SUo8nnsjmiSfc9QsLA7p2Ddh99xjt2kG/fjGOOy6qrsltKC31ePTRbPLzA377W81eEBFpijRL\nuDRLUTYXCtUl1TvtFLDTTjHGjo0RBFUEgUu8P/ooxIwZEaZPDzN9eoT16z2+/LI2E8/ippugf39X\nAdt//xijRkW3ual3WzN6dD7glvHQdjsiIk2TVm+jTz2VxW23NWwxLiVcbZvn1f3fDx3qM3RoNZde\nCtXVriJWWQmrV3tMn+5Wv//wwzCLFoV5+GF3na5dfcaMiXHYYVH22y9Ku3at91haiu/D9997lJd7\n/PvfEUpLXVL6zDNab0tEpKnSKuFKdB0ubesjW8p22zmSlwcdOgT07VvDmWfWUFUFH38cZtq0MLNm\nhVm8OMTTT2fx9NNuDFPv3j4dOwZcdFE1Bx6YWQnY009HuOWWHFat2rr//a67KlXtExFpBmmVcAEN\n3sA6CDyN35IGy8mB4cNjDB/uBofHYjB7dpgpU8LMmRNm9uwwX38d4uyz88jOdpsxH310lEGDYuTm\nQklJsDGZS0WffBJi5Ur45JNs2rULKCvziMVg/vwwb7xR9zYweHCMQYNirFvncfDBUU4+ufU2SxcR\nySRpl3CVldGg6kJDEzORbQmHN0/AysvhrbcifP55iJdeivDqq1m8+mrWxvPbtQsYMybKz38eY6+9\nfIyJtfpK7EuWeNxySw7vvOPGrTk5W50XDgc8++wGDjhAMxFFRJIlbRKuoUNjzJ4dZs0aj3btdtxV\nGARKuKT5FBTAMce4as/ll1ezYEGIKVMiWBuirAw+/TTMiy9m8eKLLgkLhQIGD3brgg0bFmPMmCgd\nOrRsm2+4IXdj9WrkyChDhkQYPryCigqP9evdkhnFxQG9e/sUF7ds20RE2pq0Sbj23dclXMuXh9h1\n1x1/E1eFS5KldmmKAQPqlkoIAvjiixBz5oRYvDjMhx+G+PjjMB9/HOaRR1wCNmSIz+jRUcaOjTJ4\nsJ/05+fbb7uVSr/6qoyCAigpKaK0VFUsEZHWkDYJV/fubtrhMcfk8+675fTrt/1tRnxfMxSl5Xge\n7L67z+67+4CrhFVVwcKFIaZNi/D2224s2Jw5OUyYkEOnTj6dOwfsuqvPyJExfv7zGP37+00aB7Zu\nHdx9dw4LF4aYPt29tHv18ikoaIYHKCIiTZI2CVfHjnXdiAceWMDKlWXbPV8VLmltOTm1q+RX8x//\n4cYfTp0a4a23IkyZEsZa9zN5ct0+kT//eYwhQ2Js2OBRUBDQvn1Au3YBPXsG9Ozps3Klx4cfhsnP\nh5ycgIICKC4OePXVCI89lkUQbP4tQwuWioikhrRJuHK2GOt75ZU53H13/WtyKeGSVFNUBEcf7WY3\n1i7KumyZx4wZYT78MMz774eZOjXC1KmNe1mGQgGHHlrD9ddX0727q2ypyisikhoanXAZY/oA44E5\nwM7AamvtLcaYDsAdwBKgL3CNtbY0fp0rgGKgPfCmtXZSQ+9v4MDNx5489lj2dhMuDZqXVFa7MOvO\nOwecfHLd8gurV3vMnRti8eIQRUVuj8i1az2WLfP47rsQP/3kUVgYMHp0lJUrQ2RlBfz0k8cee/gc\nemhU3YciIimqKRWujsDTtUmTMWaBMeYV4DxcMvWcMWYcMAE43RgzDBhtrR1njAkDi4wx06y12+8b\njNttt4C33irnF7+o+0SprqbeMS9a+FTSUadOAWPGxBgzRoPbRUQySaNrQNbaD7eoUHlAOXAkMDN+\nbAZwRPz3cbXHrbUxYBEwKpH7HDTIp1OnusHyX39df/M1aF5ERERSRbN0uhljjgXesNZ+BnQBaqtW\n64AOxpjQFsdr/9Yl0fu6/fa6bsTazXW3xfe10ryIiIikhiYPmjfGjMZ1FV4aP7QCKMIlVMXAWmut\nb4xZGT9eqxhY2dD7KSlxVz33XFi8GO65B6JRj86di7ZZyfI8iETqrpfq0qWdqUQxS5xiljjFLHGK\nWeIUs8SlW8yalHAZY44ERlprLzXGdAd6Aa8CI4DngJHxy8T/vT5+vSygH/BuQ++rtLSuODZkSBhw\n1a1p08oZMGDrNblqagri1ytP7EG1ArcgZYOGskmcYpY4xSxxilniFLPEKWaJS+WY1ZcINrrTzRiz\nD/AM8HNjzFTgJWAP4BrgEGPMtcCxwBUA1tpZwFRjzK3AvcDl1tp1DbmvuXPXb3Z5//3rBhQ/9VTW\nlqcDmqUoIiIiqaPRFS5r7Uds3kW4qfPruc6ExtxXQcHmsw0LC+G55yo4/vh8Hnoom65dAy6+uJpw\nuO4crcMlIiIiqSItUpJtjdE64IC6Ktett+bwl79svj6Ev/2df0RERERaTNomXFsemzIlvNllVbhE\nREQkVaR1SlJSUlfGmjlz895RJVwiIiKSKtIiJalvAdM5c8q58MK6zXm//rruRDdoXivNi4iISOtL\n64QrNxduuqmKq692i6Hef3/dOC7NUhQREZFUkRYpyY626DnttBoAZsyo61ZUl6KIiIikirRISXaU\ncHXtGtCtm8+SJaGN2/34vqe9FEVERCQlZETCBXDqqa7KtXBhmKVLPVW4REREJGWkRUrSkITrD3+o\nGzw/dGgh69apwiUiIiKpIWMSLoA5czbfAmj+/HA9Z4qIiIi0nIxKuHbeOeCDD+qSrpNOqklSi0RE\nREQartF7KbakRLoG+/QJWLGijGXLPHr21DpcIiIi0voyqsK16flKtkRERCRVZGTCJSIiIpJKlHCJ\niIiIJFlaJFwiIiIi6UwJl4iIiEiSKeESERERSTIlXCIiIiJJpoRLREREJMmUcImIiIgkmRIuERER\nkSRTwiUiIiKSZE3aS9EY0xUYDwy21g6LH+sA3AEsAfoC11hrS+N/uwIoBtoDb1prJzXl/kVERETS\nQVMrXPsDL29x7DZcMnVn/G8TAIwxw4DR1to/Af8BTDDGFDXx/kVERERSXpMSLmvtC0DZFoePBGbG\nf58BHBH/fVztcWttDFgEjGrK/YuIiIikg2SM4epCXRK2DuhgjAltcbz2b12ScP8iIiIiKaVJY7jq\nsQIowiVUxcBaa61vjFkZP16rGFjZkBssKcn8nse28Bibm2KWOMUscYpZ4hSzxClmiUu3mDVXwuVt\n8vurwAjgOWBk/HLt8esBjDFZQD/g3YbceGnplr2WmaWkpCjjH2NzU8wSp5glTjFLnGKWOMUscakc\ns/oSwabOUjwQ+DXQzRhzDW6A/LXAHcYYA/QBrgCw1s4yxkw1xtyKm6V4ubV23Y7uY8iQWFOaKCIi\nItLqmpRwWWvfZesqVRVwfj3nT0j0Pnbe2W9Ey0RERERSR8ovfOp5Oz5HREREJJWlfMIlIiIiku6U\ncImIiIgkWconXOpSFBERkXSX8gmXiIiISLpTwiUiIiKSZCmfcKlLUURERNJdyidcIiIiIulOCZeI\niIhIkqV8wqUuRREREUl3KZ9wiYiIiKQ7JVwiIiIiSaaES0RERCTJlHCJiIiIJJkSLhEREZEkS/mE\nS7MURUREJN2lfMIlIiIiku6UcImIiIgkWconXOpSFBERkXSX8gmXiIiISLpTwiUiIiKSZCmfcKlL\nUURERNJdpKXv0BhzMPArYAWAtfbmlm6DiIiISEtq0QqXMSYP+B/g9/FEa5Ax5qCWbIOIiIhIS2vp\nLsURwNfW2mj88gzgyO1dQV2KIiIiku5aOuHqApRtcnld/JiIiIhIxmrpMVwrgeJNLhfHj9Xrn//M\n8iArqY1KBSUlRa3dhLSjmCVOMUucYpY4xSxxilni0i1mLV3hmgnsYoypzaD2B15t4TaIiIiItCgv\nCIIWvcP4LMUTcJWtGmvtLS3aABEREZEW1uIJl4iIiEhbk/ILn4qIiIikOyVcIiIiIkmmhEtEREQk\nyZRwiYiIiCSZEi4RERGRJFPCJSJtmjGmpLXbkG6MMf2MMfsbY/QZ0kDGGO2qkiBjzE6t3YbmpGUh\nWoAxJh/4FfAZsNBau94Y41lrFfx6GGMKgYuBN6y1HxtjQtZav7Xblcriz7MLgK+AD6213+p5Vj9j\nTB7udXkksAj4p7X2s9ZtVWqLP8eOAA4FJgFTrbVl279W2xZ/LzsWGAl8Ccyw1r6v1+b2GWNOB/4A\nXGOtfSkTPgP07STJjDE/A24HioDfANcaYwr0QtuhUbh4nQ1grfWNMdrKvB7GmDHATYAPjAOOi79B\n6Xm2DcaYfYG/AF8D1+J2vdi7NduUJg4AVgHnAwuBqDEmAqDXZ71OxL0ubwQC4EpjjLHWBorZ1jap\nmoaAD4HjjTGFmfAZoIQr+YYDT1trHwD+AXQDrgK9QW3LJi+2zsBTQHtjzJEASh62zRiTC5wEPGOt\nvRf4BIik+7fBZDDGhOO/rsUlW+9ba78CpgMDW6tdqaw2ZvHX5jG4pOFk4HTgLuBq0OtzW+IxOxmY\nb61dDjyNq3JdCYrZluJVv9r3ra6412UZcKoxplO6x0sJVzMzxuxkjBlijGkXP7QvrlIDMA94FtjP\nGNM73Z88zWWTmBVv8mKrxH27+QA4xxhzqTGmU+u1MrVs+jyz1lYCPYEbjDF9cG9U+xpjbjLG7BE/\nv00n98aYHsaYPwJXGGP2t9YuAe7d5DX4OTAtfq7GdLFVzA6MvzbnAnfjuqz/BLwGHGyMGd2KTU0Z\nxphdjTHnGWOKwVXmgTnAn+KnfA+8BBQaY0wrNTOlbBqzeNUvHN9veRnwGLAEN1Tisvj5aftepoSr\nmRhjsowxJwAX4RKsl4wxnYH7gBHGmD2stVW4N3aL+4Bs07YRsxeMMbVx2Rn3RhUGdgJ6WGtXt0pD\nU8g2YvZyPLk/AZgM3Au8D9yKS7zOhLb9TdoY0x8Xr1eBpcAEY8whW4w96g/MiJ97Sis0M6VsI2Z/\nNsb8ApgC7AYMjZ86Hfg/oKY12plKjDHZuN6LX+EqgbWeBHYxxhwWfx0uA9YAP7Z8K1PLtmJmrY1Z\na2uA/YBTgRJgARCOf46m7XuZEq7msy9whLX2Gmvt73FvQDfiyqGTcaV3rLVfAHnAD63UzlSyZcx8\n3Bi39rhE61LgW+BB4BfGmFtU5doqZtXAnUAO7sMvy1r7mrV2Pu459kHrNTVlFAL9rbWfWmufwb0e\njzXGDAAwxhQB7XBv+H8DqtL5W3Qz2TJmr+MGfufi3tdqKzYDgF1wlZu2Lhv4FHgL9yW7T/z458Cj\nwH8aY3Jww0oiuK7Ztm7LmO0KEH+fXwYsx42xXIj7UnlAOr82I63dgHQWf0F9HS8bt8e9UfeNJ1VP\n4AYxvwCMB943xlyJS7Y+AVa3xVkqO4jZ48DNuJL7fFy3xQpjzOXAx8CjbbHK1YCYjQf+iXtTGmyM\nuRiXsFbhqg9tijGmH+4b81u459Fa4EdjzAhr7UxcN8XduA+++cAviE/OAC601i5o+Va3rgbE7FHc\nl8au1tr7jTG9jDHjgQrgSmvtslZqeqvZIma1s8//DgwGDC6B/09rbTXw1/iyEH+MX/0Ga+3K1mh3\na2pAzI7FxWy1Meav1tq18Qr+N8Ch8fe8tKVlIRrBGNMVGAuMAX7CjTV6G/cmvhI3K/EA4NfAe9ba\nCcaYHrgunjxr7fut0vBWlEDMTgfestb+JX69HKDEWvtda7S7NSX4PHvHWnuvMWYU8HNgevyDsk2o\n/fJijLkQKMYtjXFQ/M+/xSUMHwOPWGt/MsbcB1Rba68wxuwP7Byv5LQZjYxZ1Fp7WXwweHZ8/GCb\nUU/MRgEF1trfbHLe73DVv/+01i7a5HjEWhtt4Wa3qkbE7F5r7cItr9/CzU4KdSk2ztm46sH5wJvA\nf+O6EG8FSoFzcAPkb6i9grX2e2vtx20x2YpraMz+hOseq32hVbXFZCsukedZGMBa+4619q62lmzh\nKsfgKoCTrbXPAtfhEvhhuBmvA6mbwLIQeBfAWjujLSZbNC5m08ANBm+LyRbbjtmfcMuwjN3k9H/h\nuvv/bIy5KD5WibaYbJF4zO7eImYZkWyBEq4Giw8ixRjTATgM+CheKn4H+A54IP5N5g7gYdwYiF8C\nU1unxa2vqTHLpBdaQ+l5lhhjzAjgHtwH2164b869AOLdzzcC91tr3wAeAYYaY27DjUV6s1Ua3coU\ns8Q1IGY3AH/e5CphXI/GJ8Dj8ddwm6KYbU1dijsQz7Jvxa1zNMZa+4Ux5ilctn5S/N8jcTN6jsNN\nYf09rj/6Nmvt163R7takmCVOMUuMcat334gbkPws8BCu++tH4GJrbb/4eTnAy8AV1tr58ZnDYWvt\nilZpeCtSzBKXYMxeBK621s6Lxyy3LVbnFbP6qcK1Y2Hck+V56gY8noObPXElbgr5W7jYWloYAAAD\nf0lEQVTZTeXxkvFD1trz2tqH4CYUs8QpZompnV7/lrV2LW6CyrD42L+oMebS+HmdcNv2LAKw1q5q\ni4lDnGKWuERithjX7Vobs4xNHHZAMauHEq4dq8atAfJPYEB8/Z4K3Ifhfdbau4COQA/czB6stT+1\nVmNThGKWOMUsMRXAc9baLzc5Vjtu7XqgvzHmbtw4uA+ttbGWbmAKUswSl0jM5ihmgGJWLy0LsQPx\nJ8Nc47ZPeQW32u2b1u3rNMwYcyyuz/mu+Adkm6eYJU4xS0x8fN+3mxzqRbwig1vb5zbcgolf2Ta4\nlMi2KGaJU8wSp5jVT2O4EhBflO1+3NpGz+BWC+5orf2sVRuWwhSzxClmiTPGnIeL03G4mZ3/Ee/O\nkHooZolTzBKnmNVRhSsxpbiBfyfh1j36DFjVuk1KeYpZ4hSzBBhjugF/IL5XqbX2f1u5SSlPMUuc\nYpY4xWxzSrgSsxNu1sVZmThlNUkUs8QpZonxcUtk/Nm6/UplxxSzxClmiVPMNqEuRREREZEk0yxF\nERERkSRTwiUiIiKSZEq4RERERJJMCZeIiIhIkinhEhEREUkyLQshImnPGLMfMB7YE3gBtw1SAfCo\ntfb5HVz3DGC0tfbMpDdURNosVbhEJO1Za98HHgOWWGt/a609GTgXuN4Y8/sG3ITWxxGRpNI6XCKS\nEeKVqvOttfttcmws8Dyu8vVXYD7QCbdp7t+MMX2BB3Cbgr8NTLLWvmmMuQTYHdgAtMdtR9Lm97AU\nkcZTl6KIZLLZQD7QBbfa9TsAxpi5xpiXrbVfGGOeBEZZa38X/9sY4Ghr7SHxy7cAVwM3tMojEJGM\noIRLRDKdhxs+cZAx5hRc1aoDsBuwfBvnHw50Msb8NX7dTsAPLdRWEclQSrhEJJMNA9YDBwN7W2uP\nBTDG7A2Et3O9mdbai2ovGGPyk9pKEcl4GjQvIhnJGNMNuBPXFdgJWBM/HgJ6bnJqJfHkyxhzOjAZ\nVw0LxY8dCzRk4L2ISL00aF5E0p4xZjhwC7AX8BxuWYhi4HFr7XPGmJ2Bp4HPcYnX0cCnwNm4MV7P\nAV8AU6y1jxpjfgfsB3wL5AKXW2urW/ZRiUgmUcIlIiIikmTqUhQRERFJMiVcIiIiIkmmhEtEREQk\nyZRwiYiIiCSZEi4RERGRJFPCJSIiIpJkSrhEREREkkwJl4iIiEiS/X9VLFvOoJEv7AAAAABJRU5E\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113f90fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# @savefig es_s2_paths_lt.pdf\n",
    "data[['SX5E', 'sigma**2']].plot(subplots=True,\n",
    "                                 figsize=(10, 8),\n",
    "                                 color='blue',\n",
    "                                 grid=True);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "## select time series data with date later/earlier than given dates\n",
    "short = data[['SX5E', 'R_n']][(data.index > '2015-7-1')\n",
    "                             & (data.index <= '2015-12-31')]\n",
    "\n",
    "## calculate the realized variance in percent values\n",
    "short['sigma**2'] = 10000 * 252 * (np.cumsum(short['R_n'] ** 2)\n",
    "                                   / np.arange(len(short)))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SX5E</th>\n",
       "      <th>R_n</th>\n",
       "      <th>sigma**2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2015-07-02</th>\n",
       "      <td>3463.25</td>\n",
       "      <td>-0.009492</td>\n",
       "      <td>inf</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-07-03</th>\n",
       "      <td>3441.76</td>\n",
       "      <td>-0.006224</td>\n",
       "      <td>324.686954</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-07-06</th>\n",
       "      <td>3365.20</td>\n",
       "      <td>-0.022496</td>\n",
       "      <td>799.967421</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-07-07</th>\n",
       "      <td>3294.19</td>\n",
       "      <td>-0.021327</td>\n",
       "      <td>915.381074</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-07-08</th>\n",
       "      <td>3327.50</td>\n",
       "      <td>0.010061</td>\n",
       "      <td>750.306250</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               SX5E       R_n    sigma**2\n",
       "Date                                     \n",
       "2015-07-02  3463.25 -0.009492         inf\n",
       "2015-07-03  3441.76 -0.006224  324.686954\n",
       "2015-07-06  3365.20 -0.022496  799.967421\n",
       "2015-07-07  3294.19 -0.021327  915.381074\n",
       "2015-07-08  3327.50  0.010061  750.306250"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "short.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlwAAAHcCAYAAAADRHT1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c1db410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "short[['SX5E', 'sigma**2']].plot(subplots=True,\n",
    "                                 figsize=(10, 8),\n",
    "                                 color='blue',\n",
    "                                 grid=True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Variance Swaps"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Definition of a Variance Swap"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Numerical Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import sys\n",
    "sys.path.append('scripts/')\n",
    "from variance_swaps import generate_path "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "S0 = 100  # initial index level\n",
    "r = 0.005  # risk-less short rate\n",
    "sigma = 0.2  # instantaneous volatility\n",
    "T = 1.0 # maturity date\n",
    "M = 50  # number of time intervals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlwAAAE5CAYAAABFzf7EAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nBi5JkqSUGbgkSZJSZuCSJElK2f8AltAoAWLELpsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c1dbe90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = generate_path(S0, r, sigma, T, M)\n",
    "data.plot(figsize=(10, 5));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>index</th>\n",
       "      <th>R_t</th>\n",
       "      <th>sigma**2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>86.914274</td>\n",
       "      <td>-0.020492</td>\n",
       "      <td>462.916655</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>86.263467</td>\n",
       "      <td>-0.007516</td>\n",
       "      <td>453.668339</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>87.101314</td>\n",
       "      <td>0.009666</td>\n",
       "      <td>445.190118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>87.020414</td>\n",
       "      <td>-0.000929</td>\n",
       "      <td>436.113416</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>83.157399</td>\n",
       "      <td>-0.045408</td>\n",
       "      <td>448.009603</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        index       R_t    sigma**2\n",
       "46  86.914274 -0.020492  462.916655\n",
       "47  86.263467 -0.007516  453.668339\n",
       "48  87.101314  0.009666  445.190118\n",
       "49  87.020414 -0.000929  436.113416\n",
       "50  83.157399 -0.045408  448.009603"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data['R_t'] = np.log(data['index'] / data['index'].shift(1))\n",
    "## scaling now by M / T since returns are not necessarily daily returns\n",
    "data['sigma**2'] = 10000 * M / T * (np.cumsum(data['R_t'] ** 2)\n",
    "                                    / np.arange(len(data)))\n",
    "data.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlwAAAG7CAYAAAAWtUsXAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nEi4RERGRFPt/rT7RaE4vOQMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ccc10d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data[['index', 'sigma**2']].plot(subplots=True,\n",
    "                                 figsize=(10, 8),\n",
    "                                 color='blue',\n",
    "                                 grid=True);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "48.009603247833525"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data['sigma**2'].iloc[-1] - 20 ** 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2500.0"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Notional = 100000. / (2 * 20)\n",
    "Notional"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "120024.00811958381"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Notional * (data['sigma**2'].iloc[-1] - 20 ** 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mark-to-Market"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>index</th>\n",
       "      <th>R_t</th>\n",
       "      <th>sigma**2</th>\n",
       "      <th>V_t</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>86.914274</td>\n",
       "      <td>-0.020492</td>\n",
       "      <td>462.916655</td>\n",
       "      <td>144650.434548</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>86.263467</td>\n",
       "      <td>-0.007516</td>\n",
       "      <td>453.668339</td>\n",
       "      <td>126082.766551</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>87.101314</td>\n",
       "      <td>0.009666</td>\n",
       "      <td>445.190118</td>\n",
       "      <td>108434.594165</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>87.020414</td>\n",
       "      <td>-0.000929</td>\n",
       "      <td>436.113416</td>\n",
       "      <td>88469.022898</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>83.157399</td>\n",
       "      <td>-0.045408</td>\n",
       "      <td>448.009603</td>\n",
       "      <td>120024.008120</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        index       R_t    sigma**2            V_t\n",
       "46  86.914274 -0.020492  462.916655  144650.434548\n",
       "47  86.263467 -0.007516  453.668339  126082.766551\n",
       "48  87.101314  0.009666  445.190118  108434.594165\n",
       "49  87.020414 -0.000929  436.113416   88469.022898\n",
       "50  83.157399 -0.045408  448.009603  120024.008120"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dt = T / M\n",
    "t = np.arange(M + 1) * dt\n",
    "t\n",
    "sigma_K = 20\n",
    "data['V_t'] = Notional * np.exp(-r * (T - t)) * ((t * data['sigma**2']\n",
    "                        + (T - t) * sigma_K ** 2) / T - sigma_K ** 2) \n",
    "data.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmsAAAG7CAYAAACcmtJWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nIiIiEmH/DyCVt2sAXpx/AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ccc1ed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data[['index', 'sigma**2', 'V_t']].plot(subplots=True,\n",
    "                                 figsize=(10, 8),\n",
    "                                 color='blue',\n",
    "                                 grid=True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Vega Sensitivity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Variance Swap on the EURO STOXX 50"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "DatetimeIndex: 7475 entries, 1986-12-31 to 2015-12-30\n",
      "Data columns (total 8 columns):\n",
      "SX5P    7475 non-null float64\n",
      "SX5E    7475 non-null float64\n",
      "SXXP    7475 non-null float64\n",
      "SXXE    7475 non-null float64\n",
      "SXXF    7475 non-null float64\n",
      "SXXA    7475 non-null float64\n",
      "DK5F    7475 non-null float64\n",
      "DKXF    7475 non-null float64\n",
      "dtypes: float64(8)\n",
      "memory usage: 525.6 KB\n"
     ]
    }
   ],
   "source": [
    "es.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "DatetimeIndex: 4357 entries, 1999-01-04 to 2016-02-12\n",
      "Data columns (total 9 columns):\n",
      "V2TX    4357 non-null float64\n",
      "V6I1    3906 non-null float64\n",
      "V6I2    4357 non-null float64\n",
      "V6I3    4296 non-null float64\n",
      "V6I4    4357 non-null float64\n",
      "V6I5    4357 non-null float64\n",
      "V6I6    4340 non-null float64\n",
      "V6I7    4357 non-null float64\n",
      "V6I8    4343 non-null float64\n",
      "dtypes: float64(9)\n",
      "memory usage: 340.4 KB\n"
     ]
    }
   ],
   "source": [
    "vs_url = path + 'h_vstoxx.txt'\n",
    "try: # reading the data with pandas\n",
    "    vs = pd.read_csv(vs_url,  # filename\n",
    "                     index_col=0,  # index column (dates)\n",
    "                     parse_dates=True,  # parse date information\n",
    "                     dayfirst=True, # day before month\n",
    "                     header=2,  # header/column names\n",
    "                     sep=',')  # separator character\n",
    "except: # read stored data if there is no Internet connection\n",
    "    vs = pd.HDFStore('./source/data/V2TX.h5', 'r')\n",
    "vs.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "## 15 trading days\n",
    "T = 15."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data = pd.DataFrame(es['SX5E'][(es.index > '2015-5-31')\n",
    "                        & (es.index < '2015-6-20')])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data['V6I1'] = vs['V6I1'][(vs.index > '2015-5-31')\n",
    "                        & (vs.index < '2015-6-20')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SX5E</th>\n",
       "      <th>V6I1</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2015-06-01</th>\n",
       "      <td>3575.04</td>\n",
       "      <td>25.8710</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-06-02</th>\n",
       "      <td>3561.89</td>\n",
       "      <td>25.9232</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-06-03</th>\n",
       "      <td>3583.82</td>\n",
       "      <td>25.7958</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-06-04</th>\n",
       "      <td>3556.38</td>\n",
       "      <td>26.2418</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-06-05</th>\n",
       "      <td>3510.01</td>\n",
       "      <td>27.4496</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-06-08</th>\n",
       "      <td>3468.31</td>\n",
       "      <td>27.2996</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-06-09</th>\n",
       "      <td>3456.79</td>\n",
       "      <td>26.8020</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-06-10</th>\n",
       "      <td>3526.48</td>\n",
       "      <td>25.8610</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-06-11</th>\n",
       "      <td>3551.91</td>\n",
       "      <td>26.3897</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-06-12</th>\n",
       "      <td>3502.77</td>\n",
       "      <td>29.7725</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-06-15</th>\n",
       "      <td>3438.07</td>\n",
       "      <td>34.5593</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-06-16</th>\n",
       "      <td>3454.09</td>\n",
       "      <td>36.2222</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-06-17</th>\n",
       "      <td>3428.76</td>\n",
       "      <td>34.7235</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-06-18</th>\n",
       "      <td>3450.45</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-06-19</th>\n",
       "      <td>3455.80</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               SX5E     V6I1\n",
       "Date                        \n",
       "2015-06-01  3575.04  25.8710\n",
       "2015-06-02  3561.89  25.9232\n",
       "2015-06-03  3583.82  25.7958\n",
       "2015-06-04  3556.38  26.2418\n",
       "2015-06-05  3510.01  27.4496\n",
       "2015-06-08  3468.31  27.2996\n",
       "2015-06-09  3456.79  26.8020\n",
       "2015-06-10  3526.48  25.8610\n",
       "2015-06-11  3551.91  26.3897\n",
       "2015-06-12  3502.77  29.7725\n",
       "2015-06-15  3438.07  34.5593\n",
       "2015-06-16  3454.09  36.2222\n",
       "2015-06-17  3428.76  34.7235\n",
       "2015-06-18  3450.45      NaN\n",
       "2015-06-19  3455.80      NaN"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data = data.fillna(method='ffill')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "h5 = pd.HDFStore('data/SX5E_V6I1.h5')\n",
    "h5['SX5E_V6I1'] = data\n",
    "h5.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1932.665919369178"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data['V6I1'][0]\n",
    "sigma_K = data['V6I1'][0]\n",
    "Notional = 100000 / (2. * sigma_K)\n",
    "Notional"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data['R_t'] = np.log(data['SX5E'] / data['SX5E'].shift(1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data['sigma**2'] = 10000 * 252 * (np.cumsum(data['R_t'] ** 2)\n",
    "                                  / np.arange(len(data)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = np.arange(1, 16)\n",
    "t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "r = 0.001\n",
    "data['V_t'] = np.exp(-r * (T - t) / 365.) * ((t * data['sigma**2']\n",
    "                + (T - t) * data['V6I1'] ** 2) / T - sigma_K ** 2) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data['V_t'].loc['2015-06-01'] = 0.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SX5E</th>\n",
       "      <th>V6I1</th>\n",
       "      <th>R_t</th>\n",
       "      <th>sigma**2</th>\n",
       "      <th>V_t</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2015-06-01</th>\n",
       "      <td>3575.04</td>\n",
       "      <td>25.8710</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-06-02</th>\n",
       "      <td>3561.89</td>\n",
       "      <td>25.9232</td>\n",
       "      <td>-0.003685</td>\n",
       "      <td>34.220799</td>\n",
       "      <td>-82.332277</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-06-03</th>\n",
       "      <td>3583.82</td>\n",
       "      <td>25.7958</td>\n",
       "      <td>0.006138</td>\n",
       "      <td>64.580457</td>\n",
       "      <td>-124.049833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-06-04</th>\n",
       "      <td>3556.38</td>\n",
       "      <td>26.2418</td>\n",
       "      <td>-0.007686</td>\n",
       "      <td>92.677552</td>\n",
       "      <td>-139.593571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-06-05</th>\n",
       "      <td>3510.01</td>\n",
       "      <td>27.4496</td>\n",
       "      <td>-0.013124</td>\n",
       "      <td>178.023718</td>\n",
       "      <td>-107.644092</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-06-08</th>\n",
       "      <td>3468.31</td>\n",
       "      <td>27.2996</td>\n",
       "      <td>-0.011951</td>\n",
       "      <td>214.408816</td>\n",
       "      <td>-136.380856</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-06-09</th>\n",
       "      <td>3456.79</td>\n",
       "      <td>26.8020</td>\n",
       "      <td>-0.003327</td>\n",
       "      <td>183.323049</td>\n",
       "      <td>-200.634978</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-06-10</th>\n",
       "      <td>3526.48</td>\n",
       "      <td>25.8610</td>\n",
       "      <td>0.019960</td>\n",
       "      <td>300.555651</td>\n",
       "      <td>-196.905901</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-06-11</th>\n",
       "      <td>3551.91</td>\n",
       "      <td>26.3897</td>\n",
       "      <td>0.007185</td>\n",
       "      <td>279.249096</td>\n",
       "      <td>-223.189008</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-06-12</th>\n",
       "      <td>3502.77</td>\n",
       "      <td>29.7725</td>\n",
       "      <td>-0.013931</td>\n",
       "      <td>302.564935</td>\n",
       "      <td>-172.129074</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-06-15</th>\n",
       "      <td>3438.07</td>\n",
       "      <td>34.5593</td>\n",
       "      <td>-0.018644</td>\n",
       "      <td>359.901600</td>\n",
       "      <td>-86.887791</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-06-16</th>\n",
       "      <td>3454.09</td>\n",
       "      <td>36.2222</td>\n",
       "      <td>0.004649</td>\n",
       "      <td>332.134168</td>\n",
       "      <td>-141.190592</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-06-17</th>\n",
       "      <td>3428.76</td>\n",
       "      <td>34.7235</td>\n",
       "      <td>-0.007360</td>\n",
       "      <td>315.833038</td>\n",
       "      <td>-234.822528</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-06-18</th>\n",
       "      <td>3450.45</td>\n",
       "      <td>34.7235</td>\n",
       "      <td>0.006306</td>\n",
       "      <td>299.246550</td>\n",
       "      <td>-309.629583</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-06-19</th>\n",
       "      <td>3455.80</td>\n",
       "      <td>34.7235</td>\n",
       "      <td>0.001549</td>\n",
       "      <td>278.303868</td>\n",
       "      <td>-391.004773</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               SX5E     V6I1       R_t    sigma**2         V_t\n",
       "Date                                                          \n",
       "2015-06-01  3575.04  25.8710       NaN         NaN    0.000000\n",
       "2015-06-02  3561.89  25.9232 -0.003685   34.220799  -82.332277\n",
       "2015-06-03  3583.82  25.7958  0.006138   64.580457 -124.049833\n",
       "2015-06-04  3556.38  26.2418 -0.007686   92.677552 -139.593571\n",
       "2015-06-05  3510.01  27.4496 -0.013124  178.023718 -107.644092\n",
       "2015-06-08  3468.31  27.2996 -0.011951  214.408816 -136.380856\n",
       "2015-06-09  3456.79  26.8020 -0.003327  183.323049 -200.634978\n",
       "2015-06-10  3526.48  25.8610  0.019960  300.555651 -196.905901\n",
       "2015-06-11  3551.91  26.3897  0.007185  279.249096 -223.189008\n",
       "2015-06-12  3502.77  29.7725 -0.013931  302.564935 -172.129074\n",
       "2015-06-15  3438.07  34.5593 -0.018644  359.901600  -86.887791\n",
       "2015-06-16  3454.09  36.2222  0.004649  332.134168 -141.190592\n",
       "2015-06-17  3428.76  34.7235 -0.007360  315.833038 -234.822528\n",
       "2015-06-18  3450.45  34.7235  0.006306  299.246550 -309.629583\n",
       "2015-06-19  3455.80  34.7235  0.001549  278.303868 -391.004773"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-755681.59959400445"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Notional * data['V_t'][-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmEAAAHiCAYAAACgORugAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd4VNXWx/HvmZZJ6EpAkCIIbJCuXitNRFQEFQQsSAsg\nTREEGzZsqFxQFF8LKk0ElSLSVASRchELKEjbINJbQg2QSaad948zabRQJkwmWZ/nmSeTM3Mme4Ak\nP/ZeZy/DNE2EEEIIIcTFZYv0AIQQQgghCiIJYUIIIYQQESAhTAghhBAiAiSECSGEEEJEgIQwIYQQ\nQogIkBAmhBBCCBEBjnM9QSllALOA5UAMcCXQFQgCA4GjQC1gv9b6hdA5g4CiQHHgR631rNDxukBf\nYAtQChiotQ5e4HsSQgghhMjzzjmEhSzTWg8FUErNANpghbGftdZLQ8drhT5eBzTRWrdUStmB9Uqp\nn7XWR4GJQFOtdZJSajjQGRh7YW9JCCGEECLvO+cQprU2gfQA5gAuBzTwArBNKXUNcCnwXuiUlsAv\noXMDSqn1QGOl1DrArbVOCj3vf0AHJIQJIYQQogA475owpVRzrGXJ2VrrlcAVgKm1fhdYBEwJPbUU\n1hJluuTQsdMdF0IIIYTI9853ORKt9TxgnlJqvFKqN3AE+DX08FKgQah+LBEokuXUoqFjiaH7Jx4/\nI9M0TcMwznfYQgghhBAX02lDy/kU5tcAKmmt54YObQEqAQuAysAmrFmxzVprUyk1B2upEqWUE6gO\nLNZaJyulUpRSpbTWicDNwJwc34lhkJR0NKenCSGEEEJEXHx8kdM+ZpxrA2+lVGVgGLAScGGFqn5Y\ngW4I8G/o2Pta6z9C5wwELsG6OvI7rfXs0PE6oXO3hh4fdBZXR5oSwoQQQggRDeLji5x2JuycQ1ge\nICFMCCGEEFHhTCFMNmsVQgghhIgACWFCCCGEEBEgIUwIIYQQIgIkhAkhhBBCRICEMCGEEEKICAhX\nA+8E4GmgcZanvq61XhDaG2w01n5ilwG7tdavhV5LGnhfRIcPg8sFcXGRHokQQgghwtnA29RaNz3F\nc1sDxbXWr4QC3AGl1Gda6z1IA+9cd+wYzJ3rYMoUJ0uW2ClcGDp39tK9u48yZaJuexIhhBAiRzNm\nTGPz5n8oUaIEu3fvokSJSzAM+PLLL+jUKYHu3XsxY8Y05s6dRefO3bj55ob07NmVmJgYAGw2GyNH\nfoDf7+eDD95l5sxv6NChM+nbem3apHnjjREXPM5wNfDeAFRVSg0G0gA7MEpr7QH2ASVDpxcDdgEH\nQ5u+SgPvXBAIwKJFdqZOdTJ3roOUFGuLkquvDrBjh8GoUTF89JGLNm389O7t5aqrZPJRCCFE/pCS\ncpxPP/2I2bN/BCAYDPL228MYNOgZAoEgW7ZsBiA5+QgvvzyUMmXKAnDDDTfRtWuPbK/lcDho3/4h\n5s37Pttj//vfkrCM9bx7R4YaeA8g1MBbKeUBtmqtPaFekqOA7lrrRUqpP5VS44F4YLzWOk0pJQ28\nw8g0Yc0aG1OmOJk+3UFiolXud8UVQdq29dK2rY/KlU1SU2HaNCcffODkq6+s2y23+OnTx0ujRgGk\nLacQQohwGTIkhlmzzjtqnFKrVn6GDEk77eNOpwuAr776gjvuuItixYozaNAzAPTs2Zfu3TsyfPgb\n1Kt3dUYAA9i8eROTJk0gNTWVGjWu4sYbG5zy9YcPf4NBg54Ny3sJVwPvXlrrj7I8/BMwCEAp1Q9w\naq07h5Yjf1VKrQE2ch4NvOHMfZgKmp074Ysv4PPPYe1a69gll0Dv3tCxI9xwgw3DiMEq37P07w/9\n+sHcuTB8OCxc6GDhQgf16sGgQdC+PTidkXk/Qggh8o+4OLCF+RLAuDgX8fGuMz5n0qQv+Pjjj+nY\nsT2VK1emV69eNGzYEICnnnqS/v3707//Y9nyxKOP9qF27doEg0E6dOhA2bLxXHvttXi9yaSmevj0\n0/cxTZM9e3aGLYecT+/IbA28lVJDgDgArfVToWOtgMe01s2VUsOAY1rrV0KPzQI+01rPUEqtBppp\nrRNDNWFrtdY5LUcW+LZFx47B7NlWndfSpXZM08DlMrntNj/t2vlp1syP68z/PrP5808bH37oYuZM\nB8GgQdmyQR55xEvHjj6KSN4VQggRpUzT5OefF/D660OYPn0uhQsXZtiw1ylatCjr1q3l/fdHn/K8\njz56H7fbTZcu3dm7dw/du3fKWN7cvn0bFSpUPOsxhLttURqQoJQaHApg1YHhgE8p9U6oLuxBoE/o\n+SOAmkqpF5RSbwDbgG9Djz0MDFVKPR8ay/icvviMGbB9u0H0tby8MH4/zJ9vp2dPNzVrFqZfv1iW\nLHFw3XUBhg9PZc2aY4wdm0qLFucWwADq1w8yenQqv/56nEce8XL4sMGQIW7q1SvMkCEx7Nola5RC\nCCGiw969e3jzzVcBMAyDhg2bhAruTSZP/pz27R+kZ89H8Xq9TJo0AYDt27cye/a3Ga+xc+d2ypYt\nBxAqxs8MHRUqVGTZsqVhGWvUNfA2DOtPIj4+yDXXBLjmGutjvXoBCheO9OjCyzRh9erMOq/9+63M\nXLlykHbtfLRt66NixfD//R0+DBMmuBg92kliog2Hw+Tee626sVq1pIhfCCFE3nX06FHeeOMVypQp\nS6FChdi7dw+1atVh3769rFz5B8888wIVK17BiBFvMWfOTLp27c6dd7Zi5MhhVK2qOH78GIFAgMce\newK/38/HH/8fM2ZMo2PHLoAVyv7+exXDh793VuM500xY1IWw4cMxFy/2sWKFnd27MyfybDYTpYJc\ne22Aq6+2glm1asGwr0VfDDt2GEyb5mTqVAcbN9oBuPTSIPfe66ddOx/16wcvSgF9WhpMn+7ggw9c\naG2No3FjK4w1aSJF/EIIIURO8lUII0tN2J49BitW2Fmxws7KlTb++suOx5P5XosUMalXL8C11wa4\n5hornJUsmTffb3IyzJrlZMoUB8uWWddLxMSY3H67FbyaNg1ErFjeNOGnn+x88IGLJUussdWoEaBP\nHy+tW5/78qcQQghRUOTbEHYivx/Wr7dlC2abNtmzPadixfRlTOtWq1YwYiHC57PCzZQpTn74wUFa\nmvX3dNNNVoF9q1Y+ihbN4UUustWrbXzwgYtvv3UQCBhcdlmQHj18dOrkpVixSI9OCCGEyFsKTAg7\nlcOHYeVKOytX2jPC2eHDmX8eLpdJ7drpy5hWMCtf3sy1pTbThJUrbUyd6mTGDAcHDljrpVWrBmjX\nzs999/koXz7v/53s3Gnw8ccuJk50cvy4QaFCJg8/7OORR7xRMX4hhBDiYijQIeykk03YssXgjz/S\nZ8vsrF1rw+/P/DPKjaL/bdsMpk51MnWqk82breBVsmSQNm2s5cY6dS5OnVe4HTliFfF/8omTvXtt\n2O0m99xj1Y3VqSNF/EIIIQo2CWE58Hhg9Wo7K1bYMoLZrl0XXvR/+DDMnGnVef36q1VLFRtrcued\nftq29dG4ceTqvMLN64VvvrGK+Nevt5aAGza0wljTplLEL4QQomAKawgL7Xo/C1iOtQ37lUAC8DTQ\nOMtTX9daLwid0wKoibWpaxOsDVoDSqm6QF9gC1bLooFa65ymTy7KZq3pRf8rV1rBbNUqe0YPRshe\n9H/11VY4i4838Xph/nwHU6Y4+PFHB16vgWGYNGgQoF07H3fd5c/XG6CaJvz8s1XEv2iRFTyrVw/Q\nu7eXNm38xMTk8AJCCCFEPpIbIexZrXV6E+8ZwNdAlfRd8U94/hXAM1rrXqHPr9Jarwvd/xtoqrVO\nyus75mct+rfqy05d9J+cbHDokPXnXaNGgLZtrTqvsmWjbsbxgq1ZYxXxz5jhwO83KFXKKuLv3NlL\n8eKRHp0QQgiR+3JtOVIp5QB+AXoCrQAf1o76dmBUqJn301izXDuAS4CFWuuFSqnKwA9a66qh12oN\ndNBat83hy+aZtkWHD8Off9qzBDM7LpdJ69ZWnVetWtFZ5xVuu3YZfPKJiwkTnBw7ZhAXl1nEX6FC\nwQunQgghCo5cCWFKqebAAGC51vrlUE/JraHg1Ru4RmvdXSn1AVBVa32bUsoF/AncA5QEPtBaXx16\nvVuBl7TWjXL40nn2t7ZpIqHrDI4cgU8/hZEjrcbjNhu0a2c1Db/22kiPTgghhMgVp00GjvN9Ra31\nPGCeUmq8UqqX1vqjLA//BAwK3U8Gfgud4w017b4JWApk3QWrKJB4Nl87r8yEiXPXqRM8+CB8+62D\n//s/F199Zeerr6y90fr08dKsWSAquxwIIYQQpxIff/pC8HP+daeUqhEqtE+3BaislBqW5Vg1YHPo\n/gKgcpbHKgJaa/0vkKKUKhU6fjMw51zHI6KP0wlt2/r56acUpkxJ4ZZb/Cxb5uDhh+No2zaWxESZ\nThRCCJH/nU9hfmVgGLAScAHVgX7A41hXPyYBtYAXtdb/hM55ESvwFQaStNZvhY7XCZ27FatebFBe\nuTpSXFxr19p4440Y5s1zULp0kE8+SeWGGwKRHpYQQghxQWSfMBEVTBM++MDJa69Z+1g8/3waffr4\npM5OFHgpKRAMcsGbRgshLr4zhTCpvhF5hmFA374+vvnGQ8mSJi+/7KZLFzdHjkR6ZEJEhtY2nn46\nhpo1C3PddYX45Rd7zicJIaKGhDCR59xwQ4D581No0MDPd985adasEH//Lf9URcHg98Ps2Q7uuy+W\nhg0LMXasiyJFTA4fNrjvvljGjcsnbTaEEBLCRN5UurTJ11976N8/jW3bbLRoEccXXziJvtVzIc5O\nUpLBO++4uPbaQiQkxLJkiYOGDf2MGeNh5crjTJnioVgxk6eecjNoUAxeb6RHLIS4UFITJvK8H3+0\n07dvLIcPGzzwgI8330wlLi7SoxLiwpkmrFhhY8wYFzNnWm3OChUyad/eR0KCD6WyX6e0fbtB586x\nrF1r5/rr/YwZk0p8fNT9DBeiQJHCfBH1tm836N49lr/+slOjRoAxYzxceWXU/dsVAgCPB2bMcDBm\njItVq6w6r6pVAyQk+Gjf3nfG/rLHj0P//m6+/dbJ5ZcHGT/eQ506OV1ULoSIlIg38A6dVx1r09YH\ntNZzQ8fybANvkfekpcELL8QwbpyLwoVN3n03lVat/JEelhBnbft2g3HjnHzxhYtDhwxsNpPbb/fT\nrZuPhg0DZ30lsGnCe++5GDrUhdsN77yTSps28r0gRF50phB2vjvmLzuhgXcbwNRaNz3Vk5VSbuBJ\nYPUJD00kewPvzkBODbxFARUTA8OGpXHddQEGDXLTrVssPXt6efHFNJxSqyzyqGAQFi2yM2aMi3nz\n7JimwaWXBnn8cS+dO/soV+7cZ3QNAx5/3EuNGgF69YqlV69Y1q5NY/BgL3a5gFKIqJHrDbxDzxsB\nvAeMA/6rtZ6bHxp4i8jR2kZCgptNm+z85z8BPvnEQ9mysjwp8o4jR+Crr5yMGePi33+ta6CuvjpA\nQoKXu+/243aH5+ts3GijU6dY/v3Xxq23+vnoIw/FioXntYUQFy5X9gkLNfCeBczWWq8Evgbe0VqP\nAI4Co0LP6wgs0VpvO+ElSoWely45dEyIHCkV5IcfUmjd2sfvv9u59dY4fv5ZpgBE5K1bZ2PQoBjq\n1i3M88+72bXL4P77ffzww3G+/z6F9u3DF8AAqlUL8v33x7nlFj8LFji4445CbNokF74LEQ0uuDBf\nKTUe+CVrA2+llALmaq2vVEqNATZgdRF/BFgEzMRampynta4SOuesZ8IuaMAiX7F22YcBA6z9lYYM\ngeefR5qAi4vK54MZM+D992HxYutYhQrQpw906wYlS+b+GAIBePZZ+O9/oWhRmDQJ7ror97+uECJH\nYS3MrwFUylJcPwSrZyRa66dCx1oBj2mtm59w7kJCy5Ghz1cDzbTWiaGasLVa65xqwmQ5Upxk5Uob\n3bvHsnOnjVtu8fPBB6lceqnkdZG79u0z+PxzJxMmONm710r+jRv76dbNy223BSJSnzVtmoMBA9yk\npcFzz3l57DGvtP4SIoLCfXXkOTfwDp03AHgUWAp8qLVeLg28RTgdPAh9+8ayYIGDyy8P8umnHq65\nRi7dF+FlmvDbb3bGjHEye7YDn8+gSBGTBx7w0bWrlypVIh/+V62y0blzLLt327j3Xh8jR8reekJE\niuwTJgqMYBBGjnTx1lsuHA54+eU0unWTJuDiwqWkwPTpTj77zMnatdYUV/Xq1t5ebdv68lxz7cRE\ng4QEN7/95qBWrQDjx3soXz7qft4LEfUkhIkCZ9EiO717u9m/35oJePvt1Dz3S1JEhy1bDMaOdTF5\nspMjRwzsdpMWLfwkJPi46aaz39srErxeePbZGD7/3MWllwYZMyaVG28MRHpYQhQoEsJEgbRnj0GP\nHtZMQJUqAcaMSaV6dVmeFDkLBuGnn6y9vRYssPb2KlkySKdOPjp18kXVdiimCePGOXnuuRgAXn89\nja5dfREelRAFh4QwUWD5fPDqqzF89JGLuDiT//43lXbtZGdxcWqHDsHkyU7GjXOxdatVaP+f/1h7\ne7Vs6ScmJsIDvADLltnp1s3NgQM2OnXyMnRoGi5XpEclRP4nIUwUeLNnO3j8cTdHjxp06uTltdfS\nwrpXk4hu27YZvPuui2nTnHg8Bm63SZs2VhPt/NSXcccOqwH4mjVWA/DPPkulVKmo+x0gRFSRECYE\n8O+/BgkJsaxbZ6du3QCffuqhYsWo+/cvwmz3boM774xjzx4bFSoE6drVy4MP+rjkkkiPLHdIA3Ah\nLq6INvBWSt0JtAPWAnWAaVrrmaHXkgbe4qLyeOCZZ9xMnuykWDGT99/3cPvtUqhcUB09Cq1axbFu\nnZ1nn02jX7+C0XsxawPwmBgYOVIagAuRWyLdwLsc8ILWepdSqhSwESgeekwaeIuLKjYW3n03leuv\n9/PMM246doyjX780nnnGi+N8vxtEVPL5oHt3a2a0Sxcv/fsXnE1NT9UAfM2aNJ57rmCEUCHyiovS\nwDvL88sAv2uty0kDbxFpf/9to1u3WLZutXHzzX4++iiV0qVlebIgME0YNMjauqFZMz8TJngKbAjf\ntMlqAL55s42mTf18/LE0ABcinCLawPsET2Ltmg/SwFtEWO3aQebPP06LFj7+9z8Ht94axy+/yDRA\nQTBqlIvPP3dRu3aA0aMLbgADqFrVagB+661+fvrJwe23SwNwIS6WXG/gneXYQOCA1npc6PPKSANv\nkQeYJrz9Njz9tPX50KHw5JMUmKWpgubLL+HBB6F8eVi+HMqWjfSI8oZAAJ57Dt56y2oA/sUX0LJl\npEclRL4QvpqwExt4YxXVV1ZKDUtv4A1UAzZnOed5QGutpyilGgOrtdb/KqVSlFKltNaJwM3AnLMZ\ngyxHinDr1AmqVbPTo4ebp5+2sXChj1GjUmVZJp9ZvtxO586xFCkCn3+egtMZJCkp0qPKOwYOhEqV\nHPTv7+buu2HwYC/9+hWcWjkhckN8fJHTPpbrDbyVUo8BzwHrsNJgWeA2rfV2aeAt8prERIPevd0s\nWeKgQoUgY8bI5fv5xebNBi1aFOLoUZg82UPjxnJV7Omc2AD8nXdSKVQo0qMSIjrJPmFCnINAAIYN\nc/HOOzHExJgMHZrGww9LE/Botn+/tRfYtm02Ro708NBDsh1DThITDbp1c/Prr9IAXIgLkSuF+ULk\nV3Y7PPusly++SCE2FgYOdPPYY25SUiI9MnE+PB7o2DGWbdtsPPFEmgSws1SqlMm0aR46dfKyZo2d\n5s3jWLZMLlwRIpwkhAlxGrfdFmD+/OPUqxfg66+d3HlnHBs3yrdMNAkGoW9fNytW2Gnb1sfTT3sj\nPaSo4nLB8OFpDBuWypEjBm3bxjJ2rJPoW0ARIm+S3yhCnEGFCiazZqXQtauX9evtNGsWx+jRToJS\nJhYVXnklhtmzndx0k5933kmVJeXz1KWLj2nTPBQvbvL0024GDYrBK3lWiAsmNWFCnKXZsx08+WQM\nBw7YaNDAz3vvpVKuXNR9/xQYY8Y4eeYZN1WrBpgzJ4XixXM+R5xZ1gbg113nZ8wYaQAuRE6kJkyI\nMGjZ0s/PP6dw++1+li510LhxIb76yiFLM3nQvHl2Bg+OoWTJIJMmeSSAhUn58iazZ6dw770+fvvN\nQfPmcaxaJb9GhDhfud7AO3TOIKAoVs/IH7XWs0LHpYG3iDqmCZMnO3juOTfHjxvcdZeP//43jZIl\nJY3lBatW2bjnnjhME775JoWrr5a143AzTavrwOuvWw3A33knlfvukwsehDiV3JgJW6a1fk1r/QLW\n3mAZDbyz3NID2HVAE631i8AAYIRSKn3nsonAc1rrN4AAVgNvIfI0w4CHHvLz88/HueEGP3PmOGnU\nKI4ffpArxyJt506DDh1i8Xjgww9TJYDlEsOAfv28TJzowemE3r1jeestV6SHJUTUOecQprU2tdZD\nIaOB9+XABsBQSg1WSg1USj2llIoNndISq8k3WusAsB5oHNr01a21Tt+v+n/AXRf2doS4eCpWNPnm\nGw8vvZRKcrJBx45xDBgQw7FjkR5ZwZScDA89FEtioo1XX02jRQuZmcltt90W4IcfjlOpUpARI2J4\n7z0JYkKci4vRwPt0jbqlgbeIenY79O3r48cfU6hZM8AXX7ho0qSQNAK/yLxe6No1lg0b7PTo4eWR\nR3yRHlKBUaWKyfTpKZQrF+S112IYN84Z6SEJETXOuXdkOq31PGCeUmq8UqpX1gbewE/AoND9RCBr\n46SioWOJofsnHs/RmfowCREJ8fGwciW8/DK8+aaNe++NY+BAePVVcLsjPbr8zTQhIQGWLIF77oEP\nP3Rht8uMzMUUHw8LFkDDhvD0027KlXPz4IORHpUQed/FaOA9B3ghdK4Tq9fkYq11sjTwFvlN//5w\n0002Hn00luHDbcyZE+D991OpXVtqk3LLiBEuxo2LoX79ACNHpnDwYKRHVDCVKAGTJ9to3TqOTp3A\nND3cdpv05xQiog28Q+cMxGrQXRz4Tms9O3RcGniLfOnYMWuj0HHjXDidJk8+6eXRR704znvuWZzK\nlCkO+vaNpUKFIHPnpsieVXnAr7/aad8+FtOEL7/0cNNNEsREwSYNvIWIkJ9+svP442727bNx7bUB\n3n/fQ+XKUfc9lyctXWrn/vtjiYuDOXNSqFZNZhvzip9+stOxYywxMdY2IXXryt+NKLhks1YhIqRp\n0wCLFx/n3nt9/PGHnaZNCzFunPTeu1Ba2+jSxboAe+xYjwSwPKZp0wAffphKSgrcf3+s9FwV4jTk\nO0OIXFaiBIwencrHH1t7Kj31lJsHH4xl715pZHg+9u0zeOihWJKTDUaOTKVBA1nuyovuvtvPiBFp\nHDxoo127WLZvl3/vQpxIQpgQF0nr1n4WLz5OkyZ+fvrJanv07bdSJHYujh+Hjh1j2bHDxtNPp9Gu\nnewFlpd16OBjyJBU9uyx0a5dHPv2SRATIisJYUJcRGXKmHz1lYc330wlNRV69IilVy83hw5FemR5\nXyAAvXu7+esvOw884OOJJ7yRHpI4C336+HjiiTS2bLHRvn0shw9HekRC5B0SwoS4yAwDEhJ8LFx4\nnGuuCTB9upPGjQuxcKFs8HomL74Yw/ffO2nY0M/w4akYMqkSNZ5+2ku3bl7Wr7fz0ENxHD8e6REJ\nkTeEq4F3V611Wujx54D+Wuv40OdOYDTWfmKXAbu11q+FHpMG3qJA8/utRsj//a8Lv9+ga1cvL76Y\nRqFCkR5Z3jJ6tJPnn3dTvXqA2bNTKFo053NE3hIMwqOPupk61Unjxn4mTvQQExPpUQmR+y5WA2+U\nUo2BEkDWZNcaKK61fgUrcD2hlCoTekwaeIsCzeGAAQO8/PBDCkoFGDvWxa23FuKPP2SSOt3cuQ5e\neCGGUqWCTJrkkQAWpWw2ePfdVO64w8eiRQ569XLjl5I+UcCFq4G3VkqVAtoD751wyj6gZOh+MWAX\ncFAaeAuRqXbtID/+mEKvXl62bDFo2TKON9904S3gZU8rV9ro3dtNbCxMmuShXDnZ2yOaOZ3WlcIN\nGviZM8fJE0+4CcruIqIAC0sDb+BPYCgw+MTX1FovAv5USo0HJgHjQ0uX0sBbiCzcbnjllTSmT/dw\n+eUmb78dQ4sWcWzYUDBnxbZuNXj44VjS0mD0aA916shv6/zA7YYJEzzUrx/gyy+dvPRSjOybJwqs\nC94xPxSu/gHKkNl+qC/wKjANaAFcpbXuHaon+xV4EdgIzNNaVwm9Tmugg9a6bQ5fUr5dRb6XnGz1\noRw7FmJiYOhQ63NbAcljBw/CTTeB1vB//wd9+kR6RCLcDhyARo1g3Tqr8f2LL0Z6RELkmtPWhIWr\ngXcRrXWf0OMVgW5a62Ghz8sDe8BaylRK7cNahvxXGngLcXpvvQVNmjgYODCGgQNtTJvmZ9SoVMqX\nz9//D0lLs3ZZ19pBnz5e2rVLIykp5/NE9PnyS2vp/aWXbDgcqfTo4Yv0kIQIu4vSwFtrnaiUuhLo\nFbq9AbwDFMWqE1uDVcRfBHgsFMikgbcQOUhKMhg0KIbvvnNSuLDJ0KGp3H+/P19u0WCa0KePm2nT\nnLRs6ePTT1MLzOxfQbV1q0GrVnHs22fjvfc8PPCAVOuL/EUaeAsR5UwTvvrKweDBbo4dM7jjDh8j\nRqQRHx91379n9OabLt5+Oya0f1oKsbGRHpG4GNavt3HPPXEkJ8Nnn6Vy110SxET+IQ28hYhyhgEP\nPOBn0aLj3Hyzn++/d9K4cRzffZd/2h5NmuTg7bdjuOKKIJ9/7pEAVoDUqBFk8uQU3G7o2dPNokWy\ncbEoGCSECRFFypc3mTbNwyuvpHL0qEHnzrE8/ribo1E+Ofzzz3YGDXJTooTJ5MkplCyZv2b4RM6u\nucYK34YBnTvHyl55okCQf+VCRBmbDXr18jF/fgp16gSYPNlJkyaF+N//onP2YN06G926xWKzwfjx\nHq68UgJYQdWwYYDRo1NJS4OHHopj3Tr5FSXyN6kJEyKKeb3w9tsu3n3XRSBgcNllQWrXDlKrVoBa\ntYLUrh3HHgd/AAAgAElEQVSgYkUzzxbx791rcMcdcezebePjjz20bi21QMKqf3zssVhKlQoyc2YK\nlStH3e8pITJIYb4Q+dyKFTbefdfFqlV29uzJPntQpIhJrVqBbOFMqSBOZ4QGG3LsGNx9dxxr1th5\n/vk0+vUr4O0BRDaffupk8GA3FSoEmTUrhTJlou53lRBAmEPYuTbwDh1rAdTE2qKiCdBMax2QBt5C\nhF9SksGaNTbWrLGzZo2Nv/+2sXmzDdPM/DngcplUr27NlNWqFaRWrSA1awYoXPjijNHvh06dYpk/\n30HHjl6GD0/Ls7N1InJGjHDx1lsxKBVgxgwPl14qQUxEnzOFsPO9tGpZlv6RM7AaeE8+VQNvpdQV\nwN1a616hz6dorQOhhycCTbXWSUqp4VgNvMee55iEEEB8vMkttwS45ZZAxrFjx6xtAP7+Oz2Y2Vm/\n3sbq1Zl1ZIZhUrly9lmz2rWDYd8GwzTh2WdjmD/fQdOmft56SwKYOLUnnvBy5IjBRx+5ePDBWKZN\nS6HI6fe9FCLqXNByZKiB9y9AT2An8BLwFvCH1rpU6DlPY81y7cDakHWh1nphaNPXH7TWVUPPO+u2\nRTITJsSF8/lg0yZrpmzNGnvGx+Tk7ImodGmrzixz1izAFVecf53Z++87eeUVNzVrBpg1K+Wizb6J\n6GSaMGBADJMmubjpJj+TJ8v2JSK65MZMWHoD7wFkNvD+BBiINROWVUWgqtZ6oFLKhdXM+x6gJNLA\nW4iIcTrhqquCXHVVkPvvtwriTRO2bzcyZszSw9n8+Q7mz8/8cXG+dWYzZzp45RU3ZcoE+eILjwQw\nkSPDgBEj0khONpg920mPHrGMHeuJeE2jEOGQ2w28pwPdgYDW+rnQ8ycD3wFLkQbeQkSFpCT46y/4\n88/M28aNVmhL53JBrVpQrx7Ur2/d6tYlI2gtWwZNm1rPW7oU6tSJzHsR0SktDe6+G+bNg4cegs8/\nLzgN7UXUi2gD7wVAQpaXqAhoaeAtRHSpV8+6de1qfX78uLXHV9ZZs7VrbaxcmfnzxjBMKlUyqV07\nwJIldvx+g/HjPZQpE5Cm3OKcffwxtG8fx6RJdmJivLz5ptQTirwvog28tdYepdSLWBvDFgaStNZv\nhV5LGngLkY+cWGeWfhFAep3ZiBGpdOzoi/AoRTQ7fBjuvTeOdevs9O+fxuDBsrWJiAzThCNHICnJ\nRlKSwf79BklJ2W/799v4/Xe77BMmhIiM9Dqzo0cNatXK6f9YQuQsMdGgVas4tmyx8dJLqfTtG33B\nPhi0rlhevNjOqlV2rr8+QLt2PqmTjDC/Hw4cyBqi0u/bsoWs/futm8935qlYh8PE5zv9fK2EMCGE\nEFFnxw4riO3ebYuaGdYdOwyWLLGzeLGDxYvt7N+fvaitcGGTBx7w0bWrj6pV5T8s4eLxcEKAsp0U\nstI/HjxoZNtT8VTi4kxKljSJjzeJjw+GPlq3zOMmJUsGKV4cSpWSHfOFEELkM5s22bj77lgOHjQY\nPTqVe+7JW22vDh2CpUutwLV4sYMtWzJDV+nSQRo1CtCwoZ86dYLMnetgwgQne/daz2nY0E+3bj6a\nN/fjOO99DPK/pCSDX3+1k5h4+pmrY8dyLhwsUcIKTacOU5lhq2RJk0KFzm2M0rZICCFEvrR6tY3W\nreNITYUJEzzcemsg55NyiccDv/1mzwhdq1dndqooXNikQQN/KHgFqFYteNJFBT4ffPedgzFjnCxb\nZiWvyy8P0rmzjw4dfGHfODlaHT8O33/vYNo0JwsX2gkETs44drsVmE4XprIeu/RSE5cr98YrIUwI\nIUS+9csvdu6/PxbDgK++8nDDDRcniAUCVghMX1787Tc7aWnW71un0+TaawM0ahSgUSM/9esHz2lG\na/16G2PHOvn6aycpKQYul0mrVn4SErxce+3JAS6/8/thyRI7U6c6mTPHQUqK9QdQr16Ali39lC+f\nfRarRAkzz2xhIiFMCCFEvjZ/vp1OnWKJjYUZM1KoXTv8NVWmCf/+a2SErqVLHRw5kvn7tWZNK3Q1\nbuzn+usD57xsdSrJyfD1107GjnWyaZPVZqxOnQAJCV5at/bn6+4BpmmF3KlTnXzzjYPERCtVVagQ\npG1bH23b+qhSJe9nGAlhQggh8r0ZMxz07Onm0ktNZs5MCcsv6MTE7MX0u3ZlTq+ULx+kcWNrifHm\nmwO5ulxomtZM0JgxTr7/3kEwaFC8uMmDD/ro0sVLpUpR97v8tLZtM5g+3cnUqY6M4FmihMk991jB\n6z//ia6ZwLCGMKWUAcwClgMxwJVAV611Wujx54D+Wuv4E86rDvwGPJC+0atSqi7W7vpbsFoWDZR9\nwoQQQpyvCROcDBrk5vLLg8yalUK5cuf2O+7YMWt5Mz10rV+f2eS+RAmThg39GQX1F9JD9ULs3Gkw\nYYKTiROd7N9vwzBMbr3Vmh1r2jSQZ5bhzsXBgzBzphW8fvvNWrd1u01uv91P27Y+brklkKt1W7kp\nN3pHLtNaDwVQSs0A2gCTlVKNsXpHZvtXr5RyA08Cq094nYlAU611klJqONAZGHueYxJCCFHAderk\n48gRg1dfjaFduzi+/TaFUqVOH8R8PlixwiqmX7LEzooVVmcHsEJAkyZ+GjWygletWsE8EXDKlTMZ\nPNjLwIFeZs1yMGaMK6O/a8WKQbp08fLQQz5KnNjJOY/xeODHHx1MnepgwQIHPp+BYVhBt21bH3fd\n5ado0UiPMndd0HKkUsoB/AL0BHYCLwFvAX9orUtled4I4D1gHPBfrfXc0M77P2itq4aec9a9I2Um\nTAghxJm89pqL996LoWbNADNmpFCsmHXcNK2i9/QlxmXL7Bw/boUum82kfv1gxmzXtdcGcLsj+CbO\nwerVViH/9OlOPB4Dt9ukdWs/3bp5qVMn7+w5FgzCsmV2pk51MGuWk6NHrT/7mjUDtG3ro00bP2XK\n5J+lVcidmTCUUs2BAcBs4E/gE2Ag1kxY1ud1BJZorbcppbI+VArImqaSQ8dydKY+TEIIIcTIkeD1\nwkcf2enSpQgJCbBggXXbty/zeUpBs2bWrUkTg+LF7YD9tK+bV916q3U7eBDGjoUPPjCYPNnJ5MlO\nbrgB+vaFdu0gJiYy41u9GiZOhMmTYedO61j58ta4OnSAWrWi88/9Ql1wYb5SajzwD1CGzB6QfYFX\ngenAs4DG6iL+CLAImIm1NDlPa10l9DoyEyaEECJsgkHo08fN9OnOjGOlSgUzto1o1ChA2bL5a9Yl\nXTAICxfaQ0uVdkzToGTJIB06+Ojc2XfOtXLnY9euzAL79Nq6okVN7r7bR9u2fm64ITrr185VuAvz\nawCVshTXDwHitNZPhT6viLUcGX+KcxcSWo4Mfb4aaBZq/j0cWKu1zqkmTEKYEEKIs+LzwahRLooU\nMWnYMIBS0XVlXThs3WowbpyLyZOdHDpkYLNZBe8JCT4aNQqE9c/jyBGYPdsKXsuWWeHP6TS57TY/\nbdv6adbMHzVLvOES7hBWGRgGrARcQHWgXyhIXQn0Ct3eAN7RWntC5w0AHgWWAh9qrZcrpeoA/cic\nQRskV0cKIYQQ4efxWNt4fPaZi9WrrZmpKlUCJCT4aN/ed95F8F4vLFhgFdjPm+fI2LD2hhus4NWq\nVd6/SCA3yT5hQgghhACsixNWrLAxZoyLmTMdeL0GcXEm7dr5SEjwUaNGzoX8waDVomnqVAczZzo5\nfNjKGdWqBWjXzk+bNj7Kl4+6fJErJIQJIYQQ4iRJSQaTJjkZP97Jzp1WgdaNN1pLlS1a+HE6sz9/\n40YbU6c6mD7dyfbt1vNLlw7SurWfdu181KpV8JZ7cyIhTAghhBCn5fdbe3Z99pmTxYutjRMuuyxI\nx47Wfl2LF1t9G9OXMQsVMmnZ0trPq0GDAPaCd2HjWZMQJoQQQoiz8s8/BmPHuvjyy8x9vAAcDpOm\nTQPcd5+P22/3ExcXwUFGEQlhQgghhDgnx47BtGlOliyxc+ONAe65x0/JklGXGSJOQpgQQgghRASE\ndcf8c23grZS6E2gHrAXqANO01jNDj51PA28hhBBCiKh3vnvVLtNav6a1fgGIw2rgzWkaeJcDXtBa\nj8Bq4j0hy2MTgee01m8AAawG3kIIIYQQ+d45z4RprU1gKGQ08L4c0EqpUkB7rAbenbI8/5Msp9uB\nY6FzKwNurXVS6LH/AR2AnHbMF0IIIYSIeufdtSnUwHsWmQ28hwKDc3jNJ7F2zYcLaOAthBBCCBHt\nznkmLJ3Weh4wL9TA+3nAC/TEaj8Uq5R6Cqv+azOAUmogsFprPSP0EolA1iYJRUPHcmLExxc532EL\nIYQQQuQJ51OYn62BN1ZRfRGtdZ/Q4xWBblrrYVnOeR7QWuspobqx1Vrrf5VSKUqpUlrrROBmYM6F\nviEhhBBCiGhwPjNhaUCCUqoeWRp4A2Rp4O1WSg0G3gG6Yy1BrlNK9QHKArcBh4CHgaFKqa1Yy5jj\nL+TNCCGEEEJEi2jcJ0wIIYQQIuqdd2G+EEIIIYQ4fxLChBBCCCEiQEKYEEIIIUQESAgTQgghhIgA\nCWFCCCGEEBEgIUwIIYQQIgIkhAkhhBBCRICEMCGEEEKICJAQJoQQQggRARLChBBCCCEiQEKYEEII\nIUQESAgTQgghhIgACWFCCCGEEBEgIUwIIYQQIgIkhAkhhBBCRICEMCGEEEKICHCE+wWVUm7gV+AH\nrfVTSqkSwJvAv0AVYLDWOin03EFAUaA48KPWela4xyOEEEIIkRflxkzYa8DKLJ8PxQpYbwHfAiMA\nlFLXAU201i8CA4ARSqkiuTAeIYQQQog8J6whTCn1MLAU2Jrl8F3AL6H7/wNahO63TD+utQ4A64HG\n4RyPEEIIIUReFbblSKVUDaC61vp5pVTdLA+VAo6G7icDJZRSttDxdVmelxw6dkamaZqGYYRp1EII\nIYQQueq0oSWcNWGtgVSl1NNAA8CplHoc2AcUwQpZRYFDWuugUioxdDxdUSAxpy9iGAZJSUdzepoQ\nQgghRMTFx5++0ipsIUxrPTT9fqg4v5DW+l2llAJuBKZihbM5oafNAV4IPd8JVAcWh2s8QgghhBB5\nmWGaZlhfUCnVBugDuID/A34A3gK2A5WBZ7JcHTkQuATr6sjvtNazz+JLmDITJoQQQohoEB9f5LTL\nkWEPYReBhDAhhBBCRIUzhTDZrFUIIYQQIgIkhAkhhBBCRICEMCGEEEKICJAQJoQQQggRARLChBBC\nCCEiQEKYEEIIIfKcHj06kZs7OBw9au20MHToywAkJyeTkpKC3+9nzJjR7N27h+TkZABGjXqbTz75\nkM8/H8dLLw3m0KGDYRlDWLeoUEoZwCxgORADXAkkAE+TvS/k61rrBaFzBmHtll8cq9H3rBy+jGxR\nIYQQ4qz8/beNr792UqiQSf36AerVC1K6dNRtzSRywcqVf7Bo0U9s3vwP1113A4FAgAYNGjNz5jck\nJu6lcuUqBAJ+evTow/jxn9G9ey8AvvhiPElJSfTvP+isvs6ZtqgIZ9uidMvSd89XSs0A2gCm1rrp\niU9USl0HNNFat1RK2YH1SqmftdaSsoQQQpwXnw+++87BJ584+fXXk3/NlS0bpF69APXrB6lbN0C9\negGKF4/AQPOgIUNimDUrvNGgVSs/Q4aknfE527dvY+LEcVSpUpWNGzXVq9fgq68mMWrUaC677DK+\n+242y5YtpVo1xebN/3Dw4AH69x/E+PGfsWfPHv7zn+tZs+ZvGjZsxOHDh9m4UaNUdbp16wnA4MFP\nUqNGTZKS9lGrVl2aN7+DChWuoGTJeFau/INjx45y440NKF36MsqVK8c//2gOHz7MzTc3xOl0ZgQw\ngGDQJDY2Nix/NmH9k9Zam0B6AHMAlwMbgKpKqcFAGmAHRmmtPUBL4JfQuQGl1HqsGbOz2TlfCCGE\nyLB/v8HnnzsZN87Jnj1WtU2TJn4SEry4XPDnn3b++svOn3/amDvXydy5medWqhQMzZRZs2W1awco\nVChCb6QAWr58GS6XizZt2rN/fxJOp5PFi38GIDn5CB99NIpp0+bgcDj45JMPqVjxCipXrkLv3v14\n7LGe9OjRm2PHjnHvvXcwZ858XK4Y2rZtlRHCWrRoRYMGjQgGg3To0Jbmze9g79493HlnS3bs2E7v\n3v1YsmQRBw7s58YbbyYlJYU772zFP/9ogsEgNpv17+no0aP88cevvPbasLC879yYCUMp1RwYAMzW\nWq9USnmArVprj1KqNzAK6A6UAtZlOTU5dEwIIYQ4K6tW2fj0UxfffOPA6zUoVMikWzcv3bp5qVIl\nc+mxadMAAKYJe/YYoVBm488/7axaZWf6dCfTpzsBsNlMlLKCWd261serrgrickXkLV40Q4ak5Thr\nlRvuvrs1EyeOo0+f7lSseAWPPto/ox5s166dlChxKQ6HFVnKlr2cxMR9GeeWKVMWgMKFC1OixKXE\nxLgBsNnsAAQCAbZs+ZeNGzfgcrk4cuQIALVq1QbggQcexjAMGjVqkvGazZvfySWXXEKDBpmVVMeP\nH2PkyGE8++xLFCly+qbc5yJXQpjWeh4wTyk1XinVS2v9UZaHfwLSF1ITgazvpGjo2BmdqSO5EEKI\n/M/rhWnTYNQo+OUX61jVqvDoo9Cli0HRoi6sFsanVqoU1K2b+blpwubN8Pvv6TeDlSvtrF9vZ9Ik\n6zkul3XOf/6TeateHez23HufBcXy5WsZMOAx3O4nGTZsGEuXLsDptHPppYUoXz6eI0cOUaxYDC6X\ni8OHk4iLcxEfX4S0tCM4HLaMXGCzcdL9BQsWsGrVH4wfPx6Ab76Zki1HxMfXO2k88fE1sn1+8OBB\n/u//3ub55wdTqlQp5s2bR/PmzS/4fYc1hCmlagCVtNbpk7xbgMpKqWFa66dCx6oBm0P35wAvhM51\nAtWBxTl9HSnMF0KIgmnfPmvJcfx4J/v2WUtEzZr56d7dS5MmAWw2SEuDpKRzf+1ixaBZM+sG4PfD\nxo02/vrLxl9/2UM3G7//nllnHRdnUqeOtYSZvpx5xRUmxmlLscWp7Nixl+nTX6Zs2cvZsyeR4sXj\n2blzF2PGTKBnz7706NGHvn37UaNGTXbv3kvp0qVJSjrKhAmT2LlzF/Pm/czevXs4evQY06fPwjTh\n6NFjjB07kZtvboTX6+e5514iPj6elBQP48dPokWLVmc9voSErgSDQR5/fACmaVKoUCHq17/xrM49\n08RRuK+OrAwMA1Zi/RekOtAPeByIA5KAWsCLWut/QucMBC7BujryO611TvVgcnWkEEIUMCtWWEuO\nM2c68PkMihQxefBBHwkJXipXvnhXO6alwbp1toz6sr/+srFxo41gMDN1lShhUrduIONqzPr1A1x2\nmVyReSE2bFhH9epXATBu3KeULVuO5s3viPCozs6Zro4Mawi7SCSECSFEAZCWBt9+6+Czz1z8+ae1\n5letWoCEBB/t2/soXDjCAww5dgzWrLEK/q3Cfztbt2bfhvOyy4IZRf/WxwCXXBKhAUehUaPeJi6u\nEC6XiwMHDtCv3xMZxfJ5nYQwIYQQUWPvXoNx45xMmOBk/34bhmFy++1+unXz0ahRICqW+g4dImMJ\n888/baxaZc+4YjNdxYrphf8BKlc2KVcuSPnyQYoVIyreozg7EsKEEELkaaYJv/9uLTnOnu3A7zco\nVszkoYd8dO3q5Yorou531Un27jUy6svSlzMPHTr593PhwiblywcpV84KZuXKmVSoEMy4Hx9vEiWT\nQAIJYUIIIfKo1FSYMcPBp5+6WL3aWnKsUSNAt24+7rvPl6/36jJN2LbN4O+/7WzbZrBzp42dO23s\n2GHdP3r01L+7Y2JMLr88c+YsPayVL299LFvWxJErex+I8yEhTAghRJ6ya5e15DhxopMDB2zYbCZ3\n3OGnRw8fN90UHUuOue3IEdixw8bOnUYonGW9b7B//6mnw2w2kzJlMmfRThXUwrThuzgLEsKEEEJE\nnGnC8uV2Pv3Uydy5DgIBgxIlTB5+2EuXLj7Kl4+630cR5fFYYdYKZ1YwyxrU9uwxsl21mVXJktmX\nO8uXz5xVS69LE+EhIUwIIUTEpKTA9OlOPvvMydq11pJjrVoBunf30rq1X2ZlconPZ3UGyLrEuXNn\nZmjbtcsgLe3U+aBIkewzZ1ZIy5xVK1lS9kI7WxLChBBCXHQ7dhiMHevkiy9cHDpkYLeb3HWXn+7d\nfVx/vSw5RlowCElJRrYlzrOtS4uNzQxp2QNakAoV5OKBrC5aCFNKGcAsYDkQA1wJdMXaqPVN4F+g\nCjBYa50UOmcQVrui4sCPWutZOXwZCWFCCJFHmSYsXWotOf7wg4Ng0KBkySAdO/ro3NlH2bJR9x//\nAu3IEdi+3ZYxi2bdt2bTduywnfLqTgCXy8y2zJk5o2Zd6Vm6tFlg2j2dKYTlxvUTy7TWQwGUUjOA\n+4CGWAFrqlKqJTAC6KSUug5oorVuqZSyA+uVUj9rrSVlCSFEFDl+HKZOtZYcN2ywfrvWrRugWzcv\n997rx+2O8ADFeSlWDGrXDlK7dvCUjx87lnnxwPbtmRcPWCHNYNGiU8cMh8O6wjN7QLNm0QrSFZ5h\nfYtaaxNID2AO4HJgA9Ys2Guhp/0PGBe63xL4JXRuQCm1HmgM5NS6SAghwioYRJZPzsHhw7Bhg511\n62ysXWtj5kwnR44YOBwmbdr46NbNy7XXBmXJMZ8rXBhq1AhSowZA4KTHU1I45Sxa+v2lS08dQ+x2\n6wrPrBcLZC59Brn8chPX6fuzR41cyZlKqebAAGC21nqlUqoUkD67lQyUUErZgFLAuiynJoeOCSHE\nRXH0KPTt62b+fAcVKphUqxagSpUg1aoFqVrVuhUtGulRRk5KCmzaZGP9ehvr19vZsMG6v3dv9sQa\nHx9k0CAvnTv7KF1alhyFJS4OqlULUq0anCqkpabC7t3ZZ9GyhrXly+2Y5slJ3jBMLrvMzNjItkoV\n63u1SpUglSsHo2bmNVdCmNZ6HjBPKTVeKdUb2AcUwQpZRYFDWuugUioxdDxdUSAxp9c/U0dyIYQ4\nW7t2QevWsHo1XHklHDpk8P33J0+HlSkD1atDjRrWLf1+2bL5p72M3w+bNsGaNdbt77+tj//8Y9V5\nZVW+PNx5J9SqBbVrWx9r1rThcsVglQMLcfbKl4frrz/1Y14v7NwJW7fCtm3WR+u+wdatBitXwu+/\nZy8uMwyoVMn6Pk2/KWV9jI/PW9+zYQ1hSqkaQCWt9dzQoS1AJWAOcCMwFWgQ+pzQxxdC5zqB6sDi\nnL6OFOYLIS7U2rU2OnSIZfduG126eBk6NA2HA/bvN9i0yXbSbeFCGwsXZn+NwoXNjP99Z505u+KK\nIE5nZN5XTkzT2lvqxJmtTZtseL3ZfzuVKGFy440BqlcPUr16kBo1glSvHjjlHlJHjlykNyAKnCJF\nrLBfu/bJj/n9sHOnwebNmd+r//xjfZw718bcudmfX7y4mW3WrGpVa+a7YkUz175nzzRxFO6rIysD\nw4CVgAsrVPUDfFh1YduBysAzWa6OHAhcgnV15Hda65zqweTqSCHEBfn5ZzsJCbEcO2bw4oup9O3r\ny/F/x8ePw7//2ti4MfsP+82bTw4vDodJpUrWD/pq1TJDWpUqQQoXzsU3doIDBww2bLCxYYONdets\nbNhgha4Ttx2IjTVRKjNkVa8e5KqrgpQqJXtBieh1+DD8809mKEv/nt2yxUYgcOrv2ewBzfp4oRvX\nyj5hQggRMnmyg4ED3djt8P77qdxzj/+CXs/vh+3brdmzjRvt/PNPZlBLTj75Z2/ZsifPnFWtemGB\n5/hx0NoWmtWys369dT8xMfvSqt1uzQJkzmoFqVEjQMWKsqeTKDi8Xti2LTOUZQ1pp/qeLVXK+p5N\nD2bp4axcubP7vpEQJoQo8EwT3nrLxdtvx1CihMn48R5uuOHkQuFwfr3ExFMvbe7effJP7mLFzGwz\nZtWqBaha1bpkP/1SfZ8PNm+2ZYSs9CXF7duNk4qXK1QIhpYRAxmBq0qVIDFSsiXEKZmmtXlteijL\n+nHHjpO/x9xukyuvPDmgVa4czNZ4XkKYEKJA83phwAA3U6Y4qVgxyJdfpnDllZH72XfsGBkzZlk/\n/vuvDb8/+89rl8v6QQ/WOT5f9sdLlsw6q2WFLqWCFJHrl4QIG4/HKkc4MaBt3mwjJeXkjFWuXGYw\nGz3aJSFMCFEwHTkCCQmxLFni4JprAkyY4CE+Pm/+3PP5YOvWk2fONm2yYZpkLB9mXU7Mq+9FiIIg\nGLT6c544c7ZpU+Y2LqaJhDAhRMGzc6fBQw/FsmGDnRYtfHzwQSpxcZEe1blL/zEtRfJCRI+jR63Z\n6+bNC532O1dKMYUQ+dLq1TbuuCOODRvsPPKIl88+i84ABlb4kgAmRHQpUgTq1z91u6d0BaAzkxCi\noJk/30737rF4PPDaa6k88ogv0kMSQoiTyEyYECJfGT/eSceOsQSDMGaMBDAhRN4V7h3zK2M16l4B\nlAcOaK1fVUq9hNWYO93rWusFoXMGYbUrKg78qLWeFc4xCSEKhmAQXn/dxahRMZQsGeTzzz1cc82Z\nlwKEECKSwr0ceQkwOT1IKaXWKqVmA6bWuumJT1ZKXQc00Vq3VErZgfVKqZ+11lJ5L4Q4a2lp0K+f\nm2++cVK5cpDJk1OoVCnqLjoSQhQwYQ1hWus/TjhkAMcBQyk1GEgD7MAorbUHaAn8Ejo3oJRajzVj\nllPrIiGEAODQIejcOZblyx1cd52fCRM8XHJJpEclhBA5y7WaMKXU/7N332FOVmkfx7/pwyBFpIgg\nKoIHlSoCKhakKAJ2saOua1kbKk1RQbGCiHXVda3Y13V1fVVAsYEiRZqAskcUEQtSlTZM6vP+8Twz\nExCG4kwymfl9rivXJCdPknsyk+TOKfc5BXjPWvsN8BrwgLV2DLAeeMQ7rL53ucg6r01EZLuWLPHR\nu5BwQz8AACAASURBVHc+06YFOfnkOK+/rgRMRHJHuayONMZ0wR1mvA7AWrsw7eqPgEHe+RVAel3n\nml5bqUrbkVxEqoYZM+DEE2HFChg8GEaODOH3h7IdlojIDivzJMwY0xs40lp7nTGmIbAPcJq1doh3\nyAHAd975d4Fh3u1CQAtg8vYeQ8VaRaq28eOD/O1veUSjMGpUlL/8Jc7q1dmOSkTkj0rrOCrTivnG\nmEOAScAXuPPB8oFHAeOdXwm0BIZba7/1bjMQd0J/bWC8tXZ788FUMV+kCnvqqRA33xyhWjX45z83\ncdxx5bcJt4jIn6UNvEUk56VScOutEZ54Iky9eileemkTbduqBIWIVGylJWGqmC8iFd6mTXDllXm8\n+26IAw5I8vLLm2jSJOe+QIqIbEZJmIhUaKtW+bjggmrMnBmgc+cEzz67idq1sx2ViMifp22LRKTC\nWrzYR69e+cycGeD00+O8+qoSMBGpPJSEiUiFNGOGn1698lmyxM+AAVEee6yQSCTbUYmIlB0NR4pI\nhfN//xfkqqvySCTggQcKOe88bcItIpWPkjCRHFdQANOmBfj6az/GpOjQIZmzQ3aOA48/HuK22/Ko\nXt1h7NhNdO2qEhQiUjkpCRPJMakULFjg55NPgkyaFGDGjADR6OYroFu0SNKhQ5KOHd3Tvvs6+La5\nSLpiSCbh5psjPPNMmD33dEtQtGqlEhQiUnmVdbHWpsCdwCxgb2C1tfYOY8zuwEhgMdAMuMlau9K7\nzSDc7YpqAxOttW9v52FUJ0yqnJ9/9jFpUoBJk4JMnhxg9eqS6ZwtWyY55pgkbdsmWbjQzxdfBJg1\nK0BBQUnWVb9+qjgh69gxSatWKUIVaIefjRvhb3+rxnvvBTnwQLcERaNGKkEhIrkvY8VajTGHAg2L\nEiljzFfA+cBlwIfW2teNMX2AM621FxhjOuJWz+9jjAkAC4H21trSsiwlYVLpbdgAU6a4SdekSQEW\nLQoUX9ewYYpjjklyzDEJjj46Sb16f3wNx+Pw1Vd+ZswIFJ9+/bUkcatWzaFduySdOrlJ2aGHJqlV\nKyO/2h8sX+6jX79qzJ0b4OijEzzzzCZq1sxOLCIiZS1jxVqttTO3aPIBG4HeuD1kAFOA57zzfYCp\n3m2TxpiFwDHA9rYuEqlUEgmYO9dfnHTNnBkgkXBft/n5Dj16JDjmmATHHJPkgANS2x1aDIWgbdsU\nbdumuOyyOI4DP/7oY8aMANOnu0nZ1KkBPv/cfQvw+RxatHDnkxUlZk2alP8Q5jff+Dn33GosXern\n7LPjjBlTWKF66EREylO5zQkzxpwCvGet/cYYUx8o6r5aB+xujPED9YGv0262zmsTqfSWLPEVz+v6\n7LMga9e6GY/P59CuXao46Tr00CTh8J97LJ8PmjRxaNIkwRlnJABYuxZmzQoUJ2azZwdYuDDA88+7\nt2nQYPMhzJYty3YI8/PPA1x4YTXWrvVxww1RBgyIVfh5ayIiZalckjBjTBegi7X2Oq9pOVADN8mq\nCfxmrU0ZY1Z47UVqAiu2d/+l7UguUlH99ht89BFMnOieFi8uuW7ffeGss6BHD+ja1UedOgEgsK27\nKhP16kGzZu7jgjuEOXcuTJlSdPLz9tt+3n7bzbzy86FTJ+jc2T0dfji7PIT58svwl7+4iwzGjoUL\nLogAKgImIlVLmSdhxpjewJHW2uuMMQ2BfYB3gcOB14Ejvct4P4d5twsBLYDJ23sMzQmTXBCPuz1N\nn3zizu2aM8dPKuV29dSo4dCrV6J4btd++5UM/SWTsHJldmLed1/3dN55brmIH37wFc8p++KLAJ98\n4ufjj0t67A48cPPesr33Ln0I03Hg4YfD3HVXhJo1HZ59dhNHHZXM2u8rIlLeSus4KuuJ+YcAk4Av\ncOeD5QOPAv8HjAKWAk2BG9NWRw4E6uCujhxvrd3efDBNzJcKyXFg0SJ/8SrGKVMCbNzoZiSBgEP7\n9km6dHGTrnbtUgRzsEDM2rUwc2bJvLI5cwJs2lSSde25p5uUFc0rO/jgkt8zkYAbbojwwgthGjVK\n8corm2jRQiUoRKRyy9jqyAxREiYVxqpVPiZPLlnF+MsvJSsQ998/RZcu7oT6zp2T1KiEo+ixmFuz\nLH3C/8qVJc9Bfr6bfHbokGTOnAAffxykVaskL720iT33zLn3HhGRnaYkTKSMFBbC9OmB4t6u+fNL\n5m3VqZPiqKNKersaN86519af5jjugoP0Icz//a/kOerWLcGTT25it92yGKSISAYpCRP5k+bP93PP\nPRE++yxAYaH7egqHHTp2dAuldumSoFWrFH7/du6oCvrtN3cIc+NGH336JHJyGFZEZFcpCRPZRQUF\ncO+9EZ54IkQy6ePAA5McfXSSY49N0KlTkurVsx2hiIhUZBkr1ipSmXz8cYDBg/NYutTPPvukGD16\nE126aDNpEREpG0rCRLawapWP4cMjvP56iEDA4ZprogwcGCM/P9uRiYhIZaIkTMTjOPDaa0FuvTXC\nmjV+2rZNMmZMIa1aqYyCiIiUPSVhIsD33/sYPDiPyZOD5Oc73HFHIZdcEidQvkXrRUSkCivTJMwY\n0wB3o+421tqOXtutuJtyF7nLWvuhd90g3K2KagMTrbVvl2U8ItsTj8M//hHmvvvCbNrko1u3BPfe\nW8jee+fcghUREckxZd0T1hl4C2iT1uZYa7tueaAxpiPu/pJ9jDEBYKEx5hNrrZY+SkbMmeNnwIA8\nvvoqQN26KR56qJCTT05oE2kREcmIMk3CrLVvGGOO2aLZZ4y5CYji7kj8iLV2E9AHmOrdLmmMWYjb\nY7a9bYtE/pQNG2DUqAhPPhkilfJx7rkxbr01yu67ZzsyERGpSjIxJ+w1YIm1dpMx5grgEeASoD7w\nddpx67y27SptM0yR0owbB1dcAUuXQvPm8MQTcOyxYSCc7dBERKSKKfckzFq7MO3iR8Ag7/wKID2b\nqum1bZeKtcrOWrHCx7BhEd58M0Qw6HD99TGuuy5GtWqwcmW2oxMRkcqqtI6j8tpkpXhWjTHm3rT2\nA4DvvPPvAod7x4SAFsDkcopHqijHgZdeCtG5c3XefDNE+/ZJPviggKFD3QRMREQkW8p02yJjzNHA\nBcDxwOPA/cAwIB9YCbQEhltrv/WOHwjUwV0dOd5auyPzwbRtkeyQ777zMWhQHlOmBKle3eGWW6Jc\ndJHKToiISOZo70ipUmIxePTRMPffHyYa9dGzZ5x77onSqFHO/a+LiEiO096RUmXMnOln4MA8Fi4M\nUL9+invuKaRPH5WdEBGRikdJmFQK69fD3XdHeOaZEI7j44ILYgwbFqVWrWxHJiIisnVKwiTnTZgQ\n4IYb8li2zE/z5knGjIly2GHJbIclIiJSKiVhkrOWL/cxdGiEd94JEQo5DBoU5dprY0Qi2Y5MRERk\n+5SESc5JpeDFF0PcfnuEdet8dOyY4P77oxxwQCrboYmIiOwwJWGSU775xs/AgRGmTw9So4bD6NGF\n9OsXx19eFe9ERETKSZkmYcaYBsCdQBtrbUevbXdgJLAYaAbcZK1d6V03CLdSfm1gorX27bKMRyqP\naBQefjjMQw+FicV89O7tlp3Yc0+VnRARkdxU1v0HnYG3tmi7GzfBGuVdNwbAGNMR6GKtHQ5cD4wx\nxmhTSPmDadMCdOuWz+jREfbYw+G55zbx7LOFSsBERCSnlWkSZq19A9iykmpvYKp3fgrQyzvfp6jd\nWpsEFgLHlGU8ktvWrYPBgyOcdFI+ixb5ufjiGJ99tpFevRLZDk1ERORPy8ScsPqUJGbrgN2NMX6v\n/eu049Z5bVLFOQ68+26QoUMjLF/up0WLJGPGFNKhgybei4hI5ZGJJGw5UAM3yaoJ/GatTRljVnjt\nRWoCK3bkDkvbkVxy208/wdVXw1tvQSQCd94JgwcHCIerZzs0ERGRMlVeSVj6JjHvAocDrwNHepeL\n2ocBGGNCQAtg8o7cufaOrFySSbDWz8cfBxgzJsKGDT6OOCLBmDGF7L+/w9q12Y5QRERk15TWcVSm\nG3gbY44GLgCOBx7HnYSfj7s6cinQFLgxbXXkQKAO7urI8dbad3bgYbSBdw5zHFi61MecOQHv5Gfe\nvAAFBW7eXquWw223RTn33Lj2exQRkZxX2gbeZZqEZYiSsByycqWPuXP9zJ4dYO7cAHPn+lm9umQ9\niN/vYEyKdu2StG2bonfvBPXq5dz/pIiIyFaVloSpWKuUmQ0b4Msv3d6tOXPcpOvHHzdfgNukSYoj\nj4zTrl2Sdu1StGqVZLfdshSwiIhIFikJk10Si8HXX5f0cM2Z4+ebb/w4TknCX7duih49ErRtm+SQ\nQ5K0aZOibl31comIiICSMNkBqRR8+61/sx6uBQv8xGIlCVf16g6HH+72brm9XEkaN3Y0r0tERGQb\nlITJZhwHfvnF5/VwuUnXl18GWL++JJsKhRwOPjhV3MPVtm2K5s1TBAJZDFxERCTHKAmr4taswRtO\ndHu4Zs/2s3Ll5vO4mjdPcsIJJT1cBx2UIi8vSwGLiIhUEkrCqpCCApg3z52/5SZcAX74YfOEq1Gj\nFL17x4uHFdu0SVKzZpYCFhERqcSUhFVSjgM//+zjiy8CxacFC/wkkyXDirVrOxx7bKK4h6tt2xQN\nGmjivIiISCZkLAkzxkwFNuFW009Ya3sYY3bHLeS6GGgG3FRUyFV2TiwG8+f7ixOumTMDLFtW0ssV\nDju0a5eifftkcdK1776aOC8iIpItmewJG2+tvX2LtruBidba140xfXAr7F+QwZhy1ooVPmbOLEq4\n3OHFaLQko6pXzx1WPPTQJB06JGndWvO4REREKpJMJmGtjTGDcbcx+sJaOw7oDdzpXT8FGJvBeHJG\nMgn/+59/s6HFJUs2rzp/0EEpOnRIFp+aNFEvl4iISEWWySRspLV2pjHGD0w2xqwH6gFFexCtA2ob\nY/zW2lQG46pw1q6FWbNKEq7ZswNs2FCSUdWq5dCtW6I44WrXTlXnRUREck3GkjBr7UzvZ8oY8ylw\nLLACqIGbgNUEftuRBKy0HclzjePAokXw+eclp6+/dtuLtGgBRxxRcjLGh98fROsqREREcldGPsWN\nMQbobK19xmtqDrwBvAscDrwOdPYub1cub+BdUODW5SqaPP/FF37WrCkZWszPd+jc2e3hOvTQJO3b\nJ6lTZ/P7WL06w0GLiIjILimt4yhTXSnrgF7GmIZALWCptfZlY8x4YKSXpDUFBmUonoxILxNRNIl+\nwQI/iUTJ0GKTJim6dIkXDy0edFCKoDq4REREKj2f4+RcXSinovaEJRIwb97mE+i3LBPRunWqeMVi\nhw5J9twz555/ERER2UH16tXY5jI59bmUocsvz+Ptt0PFl+vVS9GrV0kvl8pEiIiISBElYWWoT58E\n9es7tG+vMhEiIiJSOg1HioiIiJST0oYj/du6QkRERETKj5IwERERkSxQEiYiIiKSBUrCRERERLIg\n66sjjTHdgNOA5QDW2tuzG5GIiIhI+ctqT5gxphrwD+BaL/lqbYw5NpsxiYiIiGRCtocjDweWWGsT\n3uUpQO8sxiMiIiKSEdlOwuoD6UW/1nltIiIiIpVatueErQBqpl2u6bWVxlfajuQiIiIiuSDbPWFT\ngSbGmKINFzsD72YxHhEREZGMyPq2Rd7qyL64PWBxa+0dWQ1IREREJAOynoSJiIiIVEXZHo4UERER\nqZKUhImIiIhkgZIwERERkSxQEiYiIiKSBUrCRERERLJASZiIiIhIFigJExEREckCJWEiIiIiWaAk\nTERERCQLlISJiIiIZIGSMBEREZEsUBImIiIikgVKwkRERESyQEmYiIiISBYoCRMRERHJAiVhIiIi\nIlkQzHYAxphuwGnAcgBr7e3ZjUhERESk/GW1J8wYUw34B3Ctl3y1NsYcm82YRERERDIh28ORhwNL\nrLUJ7/IUoHcW4xERERHJiGwnYfWB9WmX13ltIiIiIpVatueErQBqpl2u6bVtkzGO8803Pho2hPvv\nh7POAp+vXGMUERER2VXbzFKynYRNBZoYY0LW2jjQGXi0tBvMm+fjttuiPPhgmHPO8fH44wlGjSpk\n//2djAQsIiIisqPq1auxzet8jpPd5MVbHdkXtwcsbq29Yzs3cVauXM+SJT6GDs3jww+DhMMOV18d\n49prY1SrVv4xi4iIiOyIevVqbLMnLOtJ2C5wVq50p5E5DrzzTpBbbomwbJmfffdNMXJkIV27JrMc\nooiIiEjpSVi2J+b/KT4fnHhigilTNnLFFTF+/NHH2Wfn89e/5rFsmSaKiYiISMWV0z1hW/rqKz9D\nhuTxxRcBqld3GDIkyqWXxglme+abiIiIVEmVtidsSwcfnOLttwt48MFNRCIOt96aR/fu+cyYUal+\nTREREakEKl124vfDuecmmDKlgPPOi/H11wH69KnOgAER1qzJdnQiIiIirkqXhBXZYw+HBx6I8vbb\nBRx4YJIXXwxzxBHVefnlIKlUtqMTERGRqq7SJmFFOnVK8sEHBYwYUUhhoY/rrqvGSSdV4+uvK/2v\nLiIiIhVYlchEQiG44oo4n3++kT594syYEaRbt3xuuy3Chg3Zjk5ERESyYdOmTdxxx3D69OnOjBnT\nitv/+9/XueKKi/n220V/uM2nn37Cr7/+WiaPX+6rI40xtwLHpDXdZa390LtuEO5WRbWBidbat3fg\nLre5OnJHffhhgBtvzOOHH/zstVeKO++M0rt3QtsfiYiIZMltt0V4++2yLWdw4okJbrstWuox0WiU\nU0/txRNPPMveezcBYOLECdStW4927dr/4fi77x5Br14n0rbtITsUQ7ZXRzrW2q5pp6IErCPQxVo7\nHLgeGGOM2XZt/zLUrVuSyZM3MmBAlFWrfFx8cTXOO68aS5YoCxMREalKIpEIxx3Xk7feeqO4bc6c\nWVtNwBYu/IpFiyzjxr3NSy+N/dOPnamesDgQBQLAI9baTcaY24GotfYu77i3gCette9s5y7/dE9Y\num+/9XHDDXl8+mmQvDyH66+PceWVMSKRMnsIERERqcC+++5brrvuSt58cxzLlv3ClCmTOfvs87d6\nbFn2hJVJv58xZgJQP63JBzjAcOA1YImXeF0BPAJc4h3/ddpt1m1xH9tU2maYO6tePZg0CV59FQYM\n8HHPPRHeeCPCY49B165l9jAiIiJSQdWr1459992HWbOmsGjRIi666CJ2333ruUZeXojatfPLJBcp\nkyTMWttzBw/9CBjknV8BpP8GNb227SrLnrAi3bvDZ5/ByJERnnkmRLduPk47Lc6IEVEaNMi5XQVE\nRERkJ/TseSLPPTcWYw4kkQhuM9eIxZKsWbOBuXMXsscedcnLyyv1fktL1sp9Tpgx5t60iwcA33nn\n3wUO944JAS2AyeUdT2lq1oS7747y3nsFtGuX5I03QnTuXJ2nnw6R1J7gIiIilVb37sexZMkSjj76\n2FKP69ChE++88xbPPPNPfH9yRV8m5oTdBeQDK4GWwHBr7bfedQOBOrirI8fvwHwwKOM5YduSTMLz\nz4e4664I69b5aNMmyejRhbRtq0qvIiIismNKmxNWqTbwLg8rVvgYMSLCv/8dwudzuOiiODfdFKVW\nrYyFICIiIjlKSVgZmDIlwA03RPjmmwB166YYMSLKGWeotpiIiEhlNH36VNasWb1Z22GHHcHuu9fZ\nqftRElZGYjF4/PEw998fZtMmH0cemWDUqCjNm2uIUkRERP4o28VaK41wGK69Nsann27k+OMTfPZZ\nkC5d8rn77jAFBdmOTkRERHKJkrBd0KSJwwsvbGLs2E00aODw4IMRjj66Ou+/H8h2aCIiIpIjNBz5\nJ23cCPffH+bxx8MkEj6OOirBSScl6NkzofpiIiIiVZzmhGXA//7n56abInz2WUn92/btk/TsmeCE\nExI0b57SJH4RkQyLx2HChCD16zt07JjU+7BkXEaSMGOMD7gUuAM41lr7ddp1g3Ar4tcGJlpr3/ba\n2wBXAd/jblk00Fq7vVnuFTIJK7J0qY8JE4JMmBBk6tQAyaT73DdtmuKEE9weskMPTRLQyKWISLma\nM8fPgAF5fPWV+4bbokWSCy6I07dvXGWGJGMylYS18c6+CfQpSsKMMR1xC7T2McYEgIVAe2vtemPM\nfKCrtXalMeY+4Ctr7bPbeagKnYSl++03mDjRTcg++ihIQYH7d6hbN8Xxx7s9ZEcdlaRatSwHKiJS\niWzY4G5B99RTIVIpH2edFaewEMaNCxKP+6hWzeGUUxJceGGMdu00SiHlK6PDkcaY74HeaUnY7UDU\nWnuXd/kt4Enczbvfs9Y299pPBc6z1p6xnYfImSQsXWEhfPppgPHj3aRs1Sp3TUR+vkOXLm5C1qNH\ngjo7V35ERETSTJwYYMiQPH7+2c/++6e4775COnd2951bscLHq6+GeP75EEuXuu/BLVsmufDCOKef\nHme33bIZuVRWpSVhO7WBtzFmAu6wYREf4OD2dG1ry6H6uAlXkXVe2ypg/VbaK6W8POjRI0mPHknu\nuy/KrFl+xo8PMn58iHHj3FMg4HDYYe48sp49E+yzT87N1xMRyYrly33cckuEt94KEQw6DBgQ5brr\nYqTvrVy/vkP//jGuvjrGpEkBxo4N8d57QQYPzuO22yKcdlqciy6K06qVaj9KZuxUEmat7bkLj7EC\nSN9CvKbXtsI7v2X7dpW2I3mu6NXLPQH873/w1lvw3//6mDIlyJQpQYYNg9at4eST4ZRToF071GUu\nIrKFVAqeeQYGD4bff4fDDoMnn/TRsmUEiGzzdmee6Z5++QWeftq9zQsvhHnhhTAdOsDll8PZZ0P1\n6pn7XaTqycRwZCdgmDcnLAQsADpYa9cZY+YB3a21KyrjnLBdsXy5j/fec4csJ08OEIu5mVejRqni\nHrIjjkgSCmU50Cpm9WofCxb42XvvFPvt5yghFqkAFi3yM2hQhKlTg+y2m8Mtt0S56KI4/l2ogJlM\nwocfBnj++TAffBAglfJRo4ZD375xLrggzkEHqXdMdk2mJubXxl3pOAB4AXjZWjvDu24gUAd3deT4\noqFLY0xroD+wxLt+UK6vjixLGzbAxx8HGT8+yMSJQdaudf+OtWo5dOvmziPr2jVBjdzvGKxwfvzR\nx7RpAaZNCzB9eoBvvilZzrr77g7t2iU55JAk7dsnadcuqbl8IhkUi8Ejj4R54IEwsZiPE06IM3Jk\nlIYNy+bz7KeffLz4YoiXXgqxfLmb0XXokOTCC2OceGJCi6lkp6hOWCUQj8O0aSUT+3/6yX1jCIcd\njjwyWVz+QgVid14qBdb6ixOu6dMD/PxzyVfp/HyHQw9N0rZtkh9/9DNrVqB4Um+RffdNbZaUtWyZ\n2mwuioiUjenTAwwaFMHaAA0apBg5Mkrv3olyeax4HN5/P8jzz4f45JMAjuOjdm2Hs85ye8e0b7Ds\nCCVhlYzjwIIF/uKEbMGCkl6aQw4pScgOOEBLr7cmFoMvv/R7CVeQGTMC/PZbyRO1xx4pOnVK0qlT\nksMOcxOqLYd/V670MXeum5DNnh1gzpxAcU8lQCjk0LJlarMes6ZNNYwpsqvWrYM77ogwdmwYgIsu\ninHLLVFq1tzODcvIkiVu79jLL4eKV7cfcUSCCy+M06tXgsi2p59JFackrJJbutSdRzZ+/B8LxBZV\n7K/KBWI3bICZM0uGFmfPDrBpU8lrokmTVHHCddhhSZo12/nk1XFg8WLfZknZggV+4vGSO6pd26Ft\n2/RhzBR16+bc608k4955J8jQoRGWL/djjLvCvFOnZFZiicVg/Hi3d+zTT921bXvskeKcc+L06xdn\nv/30mpbNKQmrQkorEHvccQk6dkyy114OjRun2Gsvh/z8LAdcDlau9BUPK06fHmD+fH9xYurzObRo\nkSpOuDp1cp+P8lBY6PZYzpkTKE7OlizZfBizSZMU7du7iVm7dklatUppvomI55dffAwdGmH8+BDh\nsMOAAW55iXA425G5vvvOx/PPh/nXv4KsWeO+to8+2u0d69kzoQVUAigJq7KKCsQWbaO0cuUflwzV\nqZOiUSOHRo22/rNBA4fgThUyySzHcXsCi3q5pk0L8O23JV1+oZBD27YpDjssQadOSTp2TFK7dvbi\nXb36j8OY6UOhwaDDwQenD2Om2H//1C6t9hLJVckkPPdciLvuirBhg4/DD08wZkwhzZpVzM+rwkK3\nt+7550NMm+a+Ydavn+K88+Kcf36cvfeumHFLZigJE1Ipdx81a/38/LOfn3/2bfYzfXguXSDg0LCh\nw157pWjc2P3ZqFFJT1rjxilq185cDbNUChYu9G+WdP36a0mGUr26Q4cOJUOL7dpV7G2hHAe+/97H\n7NklSdn8+f7i0iQANWu6w5hFPWaHHJKiXr2ce92K7JCFC939HmfNClCrlsOtt0Y599xdKzuRDdb6\nef75EK+9FmLtWh8+n0PXru7Kyu7dkxX6S62UDyVhUirHcYcx05Oyn37y88svvuKfy5b5SKW2/n+U\nn//HHrT0JK1hQ2eXE6FoFObOLRlanDFj8wnwdeuWDC0edliSgw5K5fybXDQKX33lL07MZs8OsHjx\n5p9Ae++d8hIyNylr1SpZKYeWpeooLIQHHgjzyCNhEgkfp5wS5447ojm74rugAP7v/4KMHRtm1iy3\nd36vvdzesfPOi5fbNAipeJSEyZ+WSMCvv/q22otW9DN9WG1Ldeu6yVl6j1rjxiVJW/36DoEArF8P\nX3xR0ss1Z06AwsKS+91336KkK8FhhyWrTOHU336DOXMCaYmZv3gOCrg9li1bprjggjhnnhnXSi3J\nKVOmBBg4MI/Fi/00bpxi1KhCevTIzsT78rBggds79vrrITZs8OH3Oxx3nDt3rEuXqrtoqqrIVLFW\nH3ApcAdwbFrF/H2ACcAy79BZ1trB3nVtcAu8fo+7b+RAFWvNXRs3wi+/+PnpJ98ffv78s9uj0QbO\nhwAAIABJREFUlp5QpQsGHerVc1i+vKTHzedz50cVrVzs1CnJnnvm3JeGcuE48MMPvs16y7780l2N\n2bBhiiuvjHH++XFtuSIV2m+/wYgREV5+OYzf73DppXFuuCFaaTfS3rAB3nzT3UD8yy/dzGvvvVP0\n6xfn4otjGSu3IZmVqSSsjXf2TaDPFknYMdba57dym/lAV2vtSm1bVPk5jjsxvWiYc8uetGXLfDRu\nXDK82KFDUm9KO2HZMh+PPx7m+edDFBT42GOPFJdd5r6516qV7ehESjgO/Pe/QW6+OcKqVX4OPjjJ\n/fcX0q5d1Sl+Oneu2zv2xhvu67Vx4xR//3shRxxReXoAxZXR4cit7B25DzAGmIq7bdHL1tqFxpim\nwHvW2ubecacC51lrz9jOQygJEynF6tU+nnwyxNNPh1m71t3/7uKLY1x2WVwT+iXrli71ccMNeXz4\nYZC8PIfBg2P87W+xKlvOYd06eOyxMA89FCaVgiuuiDN0aFRTCiqRMkvCjDETcIcNi28POMDwtP0g\nt0zCqgH7eolXfWAa0BY4CHjMWnuId1w34FZr7dHbCUNJmMgOWL8ennsuzOOPuxW+8/Iczj8/zlVX\nxWjUSMmYZFYiAU89FWLkyAgFBT6OPjrB6NGFKm7qmTnTz1VXVeP77/0ceGCSxx4r5OCDq07PYGWW\n1Z6wrVw/FRgC/Ay8b61t5rXvcE9YWcYrUtlt2gTPPAP33gtLl0IoBP36wQ03wAEHZDs6qQrmzIFL\nL4VZs2CPPeCBB+D88zNX2iZXbNgAgwbBE09AOAx33QXXX48m7ue+rA5H9gPmWGsXGGNCwHdAZ2vt\nj8aYeUB3a+0KzQkTKV/xOPznP0EefjjMt98G8PsdTjopQf/+MVq21DduKXsFBXDvvRGeeCJEMumj\nb984I0ZEtV3XdkycGOC66/JYudLPEUckeOSRQhV8zWGZmphfG3el4wDgBdy5XzOMMccClwFzgWbA\nZ9basd5tWgP9gSVAHWCQVkeKlK9kEsaNC/LAA+Hizd+POy7BtddG6dBByZiUjY8/DjB4cB5Ll/rZ\nZ58Uo0cX0qWLJp3vqFWrfAwc6G7ZVKOGwz33FNK3b0K9hzlIdcJE5A8cBz76KMADD4SZMcOtcNu5\nc4Lrrotx9NFJvdnLLlm1ysfw4RFefz1EIOBwxRUxBg2KqZjwLnAcePXVIDfdlMfGjT5OPDHO6NGF\n1KmT7chkZygJE5FSTZ0a4MEHw3z8sZuMHXJIkmuvjXH88Ymc2S5Gsstx4F//CnLrrXn89puPtm2T\njBlTSKtW6l39s374wcfVV+cxfXqQBg1SPPRQIV27qlcxVygJE5Ed8uWXfh58MMy777r1Alq0SNK/\nf4xTTknk/HZQUn4WL/YxeHAen34aJD/fYejQKJdcEteE8jKUTMKjj4YZNSpMPO7j4otjDB8eVQ9j\nDlASJiI7xVo/Dz8c5o03giSTPvbZJ8U118Q46yxtiSSuwkIYPz7IK6+EmDQpgOP46N49wahRmkRe\nnubP93PllXlYG2D//VM89timKlXkNhcpCRORXfLDDz4efTTMK6+EiEZ97LmnuyVSv37aEqkqchy3\n0vsrr4R4880Qa9e6ny2HHprkiiti9OmjieOZUFgId90V4YknwgSDDgMHxrj22ph6qysoJWEi8qcs\nX+5uifTcc+4WK3XqlGyJVLt2tqOT8rZypY/XXw/y6qshFi50xxgbNEhx5plxzj47QfPm6onJhsmT\nA/Tvn8cvv/hp3z7Jo49uomnTnPtMr/SUhIlImfjtN3jyyTBPPRXm99997Labw1/+EuPyy+PUr59z\n7yVSingcPvwwwMsvh/jggyCJhI9QyOH44xOce26cLl2S6nmpAH7/HW68MY833giRn+9w++1R+vWL\nq0eyAlESJiJlasMGGDs2xOOPh1mxwt0S6bzz3C2RGjfOufcUSfO//7nDjf/+d5BVq9ylsS1bJjnn\nnDinnZZgjz30962I3nwzyJAheaxd66NHjwT3319Igwb6W1UEmSrWej+w0Tu1Aa611q7wrhsE1MTd\nwHuitfZtr70NboHX73H3pByoYq0iuaOwEF55JcSjj4ZZutRPMOjQt2+Ca66J0qyZPgByxdq18Oab\nIV59NcTs2e5w4+67O5x+epxzzomrzESO+OUXH9dc465S3WOPFGPGROnVK5HtsKq8TCVht1trh3vn\nhwCNrLXXGmM64m7w3ccYEwAWAu2tteuNMfOBrtbaldq2SCR3xePwxhvulkiLFgXw+Uq2RNIHeMWU\nSsGnnwZ45ZUQ48YFKSz04fc7dO3q9nodd1xCK2FzUCoFTz8d4o47IhQW+jj33Bh33hllt92yHVnV\nlfHhSGPMjUANa+3Nxpjbgai19i7vureAJ4Gvgfestc299h3ewFtJmEjFlEq5WyI9+GCYefPcHpXu\n3RNcd12Ujh23n4w5jpvQxWIQjfq8n5ufj8V83s/NzxcW+v7QVnS7ovNbtqdfn5fnDru1apWidesk\nBx2Uolq18n7GMm/JEh+vvhritddC/PSTO9y4//4pzjknTt++cRo2VA9mZWCtW8pi/vwATZqk+Pvf\nCznsMBV4zYbSkrCdmlZpjJmAO2xYxAc4uD1d73jH1AZ6AKd5x9THTbiKrPPaVgHrt9IuIjnK74c+\nfRL07p3g448DPPRQmA8+CPLBB0EOPjhJtWpslhT9McnK7GziYNAhHIZIBDZuhLlzS6qLBgIOBxyQ\nKk7KWrdO0bJlMid7FDZuhHfecVc3Tpnivu1Xr+5w3nkxzjknTocOKU3krmSMSTF+fAH33Rfm4YfD\nnHxyNa65JsaQITHC4WxHJ0V2Kgmz1vYs7XpjTE3gEeAv1tq1XvMKoEbaYTW9thXe+S3bt6tevRrb\nP0hEsuqss9zTZ5/B3XfDhAkBAgE34Sk65eVBjRqbt23tlJe3/WN25dhAoCTziMdh4UKYPbvo5GPO\nnAALFwZ47TV3BwGfDw44AA45pOTUrh3svnu2nuVtcxyYOhWefRb+9S9Y733l7dIF/vIXOP10H9Wr\nhwF9IldmDzwAZ5wBF1wADz8cYfLkCC++CAcfnO3IBMp2Tlhd4AFgiLV2mTHmNGvtG8aYTsAwb05Y\nCFgAdLDWrjPGzAO6W2tXaE6YSOXmOORcb0syCYsX+5k3z8+XXwaYP9/PvHkB1q/f/Bdp0qSkt6x1\na3dIs1697Azr/fqrj9deC/Hqq0G+/dbt2WvcuKimV5x999VwY1W0YQMMGxbhpZfCRCIOt9wS5dJL\n49obNgMyNTF/FhAA1uAOU66z1p7sXTcQqIO7OnJ82tBla6A/sMS7fpBWR4pIRZZKuTsJzJ8fYN48\nNymbP9/P6tWbf5o1bJiidesUrVolixO0hg2dcklEo1F4/313C6GPPgqQSvnIy3Po1SvBOefEOeqo\npD5sBXC3mho4MMKqVX6OOirBI48UstdeSszLk+qEiYiUI8dxywPMm+cmZkUJ2q+/bp751K2b2qy3\nrHXrJE2a7HpiNn++W9PrP/8J8dtv7p0cckiSs8+Oc+qpcWrV+rO/mVRGK1b4GDAgj/ffD1KrlsOo\nUYWcdppKWZQXJWEiIlmwfLmPBQv8myVnS5dunpjVquVslpS1bp2kaVNnmz1Xa9bAf/4T4pVXQixY\n4A431q2b4swzE5x9dpwWLVQSRLbPceDFF0MMGxahoMDHqafGGTWqUNuQlQMlYSIiFcSaNXg9ZSVz\nzBYv3jzjql7doWXLZNpwZopffvHxyishJkwIEo/7CAYdevRwhxu7dUsSCmXpF5Kctnixj6uuqsas\nWQEaNkzx8MOFHHOMSlmUJSVhIiIV2Pr1sGDB5nPMvvnGTyr1x/fuAw90i6mefnoia5P/pXJJJODh\nh8Pcd1+YRMLHZZfFuPnmaKWsk5cNSsJERHJMQQF8/XVJUpafD337xmnTRjW9pHzMnesWeP322wDG\nJHnssULteFEGlISJiIjIdhUUwJ13RnjqqTChkMOQITGuvjpGILD928rWKQkTERGRHfbRRwGuvTaP\n5cv9dOyYYPToKAceqF6xXVFaEqbKMSIiIrKZrl2TTJq0kZNOijNjRpBjj81n4MAIy5drLLwslWWx\n1vuBjd6pDXCtVwl/H2ACsMw7dJa1drB3mzbAVcD3uPtGDlSxVhERkYrBceDDDwPcdluEb74JkJ/v\ncM01Mf72txjVq2c7utyQqZ6wDdbaYdbakcAc4Oa06+6x1nb1ToPT2l8EbrbW3gMkgQvLMB4RERH5\nE3w+6N49ySefFDB6dCH5+Q6jRkU4/PDqvPpqkKSqWfwpZZaEWWuHb3G/G9Iun2SMGWiMucMYcyCA\nMaYpkGetXekdMwXoXVbxiIiISNkIBuHCC+NMn76R66+P8vvvPvr3r0b37vlMmqRZ+7squDMHG2Mm\n4A4bFvEBDjA8bT/I2kAP4HTvmJW4G3gvNMbUB6YZY9p695M+rrhui/sWERGRCqRGDRg6NMYFF8S5\n554Ir70Wom/ffLp3TzB8eFQ7NuykMl0daYypCTyKO8S4dBvHTAWGAD8D71trm3ntpwLnWWvP2M7D\n5NxyThERkcpo9mwYNAg+/hj8frj0UhgxAho0yHZkFUr5l6gwxtQFHgCGWGuXGWNOs9a+YYzpB8yx\n1i4wxoSA74DO1tofjTHzgO7eBP77gK+stc9u56E0MV9ERKSCcByYODHAiBERFi0KUL26Q//+MS6/\nPEZ+frajy76M1AkzxswCAsAa3KxvnbX2ZGPMscBlwFygGfCZtXasd5vWQH9gCVAHGKTVkSIiIrkn\nkYAXXggxenSYVav87LVXiqFDo/Ttm9jmhvRVgYq1ioiISEasX+/uRfnEE2EKC320apVkxIgoRx5Z\nNZdSKgkTERGRjPrpJx933x3h9ddDABx3nDt5/4ADqtbkfSVhIiIikhVffunn1lsjfP55kEDAoV+/\nOIMHx6hXL+fyj12iJExERESyxnHgvfcCjBiRx3ff+dltN4drr41x2WUxqlXLdnTlS0mYiIiIZF08\nDs8/H+K++8KsXu2nUaMUN90U5fTTK+/kfSVhIiIiUmGsWwcPPRTmn/8ME436aNPGnbx/xBGVb/K+\nkjARERGpcJYudSfvv/GGO3m/Z884w4dHadYs53KTbVISJiIiIhXWnDnu5P1p09zJ+xdeGGfQoBh1\n6+ZcjvIHmSrW2h9oCSwCOgMjrbXTvOsGATWB2sBEa+3bXnsb4Crge9x9IweqWKuIiEjV4zgwfnyQ\n22+PsHixnxo1Sibv5+VlO7pdV1oSVpbT4MLANdba0cBzwO0AxpiOQBdr7XDgemCMMaaGd5sXcfeZ\nvAdIAheWYTwiIiKSI3w+6NUrweTJG7n77kJCIYc774xwxBHV+c9/gqQqYXmxMkvCrLX3WWuj3sVm\nwALvfB9gqndMElgIHGOMaQrkWWtXesdNAXqXVTwiIiKSe8JhuOSSONOnb+Sqq2KsWOHjiiuqccIJ\n+UybFsh2eGUquDMHG2Mm4A4bFvEBDjDcWvuOMaYBMBRoC5zmHVMf+DrtNuu8tlXA+q20i4iISBVX\nqxbcemuUiy6KcffdEd58M8RJJ+XTq1ecYcOi7L9/7s8X26kkzFrbczvXLweu8zbtHg90AlYANdIO\nq+m1rfDOb9m+XfXq1dj+QSIiIpLz6tWDN96A6dNh4EAYNy7E+++HuPJKGDYM6tbNdoS7bqeSsNIY\nYwZZa+/zLi4B9vPOvwsM844JAS2AydbadcaYAmNMfWvtCtzJ/O/uyGNpYr6IiEjV0rSpm4y9806Q\nO+6I8PDDfp57zuH666NcemmccDjbEW5daR1HZbk68mEgCqwGWgOvpK2CHAjUwV0dOd5a+47X3hro\nj5u01QEGaXWkiIiIlCYWg2efDTFmTITff/fRvHmSkSOjHHVUxSv2qjphIiIiUun8/juMHBnhuedC\npFI+Tj01zogRUfbcs+LkNkrCREREpNKaN8/PkCF5zJ4dYLfdHIYMiXLJJXGCZTbpatdlqk6YiIiI\nSMa1bp1i3LgCxowpJBSC4cPz6Nat4pe0UBImIiIiOc/vh3794nz++UbOPz/GwoUBTjopn2uuyWPl\nym12RmWVkjARERGpNPbYw+H++6OMG7eRVq2S/OtfIY44ojrPPBMiWcHm7SsJExERkUrn0ENTvP9+\nAffcU4jjwI035tGzZz6zZ1ec1KfiRCIiIiJShgIB+Otf3SHKvn3jfPllgBNOyGfgwAhr1mQ7OiVh\nIiIiUsnVr+/w6KOFvPVWAcakeOGFMEccUZ0XXwxldWPwsizW2h9oCSzCrX4/0lo7zRizDzABWOYd\nOstaO9i7TRvgKuB73H0jB6pYq4iIiJSXeByefDLE6NERNm700b59knvvLaRVq/LJxjJVoiIMXGOt\nHQ08B9yedt091tqu3mlwWvuLwM3W2nuAJHBhGcYjIiIisplQCK680h2iPPnkOLNmBejRI5+hQyOs\nXZvZWMosCbPW3metjXoXmwFfpV19kjFmoDHmDmPMgQDGmKZAnrV2pXfMFKB3WcUjIiIisi0NGzo8\n+WQh//53Afvt5/D00+4Q5WuvBclUHfudqiVrjJmAO2xYxAc4wHBr7TvGmAbAUKAtcJp3zEpgmLV2\noTGmPjDNGNPWu5/0ccV1W9z3NpW2GaaIiIjIjjrjDDjxRBgzBu6808/VV1fjtdfg0UehZcvyfexy\n2bbIGHMs7pywTlu5biowBPgZeN9a28xrPxU4z1p7xnbuXnPCREREpMwtXepj2LAI48eHCAQcLrss\nzuDBUXbbbdfvMyNzwowxg9IuLgH289r7GWNaeudDQCNgibV2MVDg9Y6BO5n/3bKKR0RERGRnNGni\nMHZsIS+9VEDjxg6PP+4OUb71VvkMUZbl6siHgSiwGmgNvGKtfdvrFbsMmIs7V+wza+1Y7zatgf64\nSVsdYJBWR4qIiEi2bdoEjzwS5pFHwkSjPo4+OsHIkYU0a7ZzeVNpPWHlMhxZzpSEiYiISEYsXuzj\n5pvz+PDDIKGQw5VXxrj++hj5+Tt2+0yVqBARERGpVJo2dXj55U08++wm6td3eOihCEceWZ1x4/78\nEKWSMBEREZFS+HzQu3eCzz7bSP/+UZYv93HRRdU477xqLFmyzY6u7d+vhiNFREREdtyiRX5uvDHC\np58GiUQc+vePcc01MfLy/nishiNFREREykjz5ilef30TTzyxidq1HUaPjnD00dX58MPATt2PkjAR\nERGRneTzwamnJvj8841cfnmMH3/0cc45+Vx0UR4//bRjQ5QajhQRERH5k77+2s8NN0SYPj1Ifr7D\ngAEx/va3GI0aZbBEhTHmZuA6a229tLZBQE2gNjDRWvu2194GuAr4HnfLooGqEyYiIiK5yHHgtdeC\njBgRYdUqP82bJ/nmm0Bm5oQZY44BdsfdT7KorSPQxVo7HLgeGGOMKdr88UXgZmvtPUASuLAs4xER\nERHJFJ8PzjrLHaL8y19ifPtt6WlWWW5bVB84E3h4i6v6AFMBrLVJYCFwjDGmKZBnrV3pHTcF6F1W\n8YiIiIhkQ+3aMGpUlA8/LCj1uODO3KkxZgLusGERH26v163AycBA3J6wdPWBr9Mur/PaVgHrt9Iu\nIiIikvNatix9htVOJWHW2p5bazfGtAdiwOW4e0BWM8YMAd4AVgA10g6v6bWt8M5v2b49vnr1amz/\nKBEREZEKbKeSsG2x1s4CZgEYY/YB/mqtvde7/C4wzDsfAloAk62164wxBcaY+tbaFUBn4N2yiEdE\nRESkoivT1ZHGmP2Bv3mne4AHrLWbjDEDcXvIagPjrbXveMe3BvoDS7zrB+3A6kgRERGRnJeLdcJE\nREREcp4q5ouIiIhkgZKwKswYs+tbv5czY8zObcCVQcaYatmOYUdU5L+viGxbRX7tVuTYcpGGI8uQ\nMeYg4CxgHDDPWrspyyFtxovvcmA28F9r7dosh7QZY8zBwF3W2lO8yz5rbYX5BzXGdAEuAf5urZ2W\n5XD+wBhzIHApMA94swL+fVvgvj4mATOttRsq0t/YGLOftfb7bMexLRXpudoaY0xTa+3ibMexLcaY\nDkDUWjsv27FsjTHmEKCdtfbpbMeyJWPMscAA4BSv3meF4r33rbTWrsp2LDurTFZHVnXGmN2Bc3Br\npq0HrgQ+B57IZlxFvB0KrgY2AtOBE4C9gTuzGRf84YOlE3CSMeZGa+1ISurQZZUxpjbuQpMGwEMV\nKQHzvpX6gBtxd52YCpwI1ANGZzE0YLNvzQO8n/8D+uEmi+dlJagtGGPqAr1wi0gvAxZZa8caY/wV\nYaGQMaYm8HfgfdxdRioU7/k7ATjFGLMYmGStfaeiJI3GmCbAzcC+wHVeW4X420Lx58dxuJUDvjLG\n1KooX6CMMXsDNwF1gXygKzAxq0GlMcbsifvc9QQcY8wn1tonK8r/3o7QcOSfYIzxecNmHYAW1trH\nrbX3Ad/gFp/NatetF18Y2A+oZa192Fr7MvAVMC3tuKz8H3jPTfrQ3jrclbUDjDHVrbUpr6xJVnjP\nXwg4AFhjrT0N2GiMucEY089bDZzt5y8f93XcGHjLWvtv3ETsm6K4KkB8QWAf4DFr7b+AB4GzjDFd\nrLVOtuJLcxpQHbeX82PgfmPM3t7/X0UYemmEW2vxCmNMve0dnEnGmENxv8wtwP2itwbo4CU5Wf8Q\n9HrXHwLet9YeD2wyxhS9ZirK0NrhQIG1dgSwGIgYYyKQ9c+PE3Brfc601vbFfR6XZiuebbgKyMP9\nQvcesHcuJWCQoSTMGNPeGFMnE4+VKcaYHrj1z0biJg8fp10dBwIA2fpnSIvvbtxE51Ov/SDcnpKu\nxphHvRgz/o3Qi+9mYKTXDQ/QHngJt17cO8aYs3DLmmRc2vN3D+7rJOVtRL8vMNmL9QnI6vN3C3AH\n7peANsCJxpizge643wzfrkDxnQ909K7+CfjAuy5b8R3o/czDTbK/tdY61toPgbeAZzId0zbiCwIh\n3N5DgMuyFlQa730E3ALbG621c6y1y3B7251s9zKlxbca+BKYb4y5Avd5HIP3v5ctaX/fMO7/X8IY\ncz7QzYttbBZjK3ruvgL+mTY8ehhwTHaiKpH23NUGWgIrvM/Zvb1DjvKuz1gCa4xpuquPV25JWFFA\n3ljyJNxvSZWCV9/sGOAB4DfcF3Z6j81+wOvGmAOMMe2822TyHyI9vtXABZTsWhADLsZNHk80xpye\nqbi2Et9DwC+43/CvwK0XF8H9ttUKWJu2t2g24nsA95v9aV5cH1trX7fWTgVGANWNMYdlMb4Hvfh6\nAZ8BM3GHxW+01l4BtDPG9K0A8XXB/ZsOMcacA5yKu8fsd8bdQzaTsYWNMaOB94wx+1trC3GHc69M\nO+xaYH9jTOtMf4naIr6m1toEsMRauwH3S8uFaR+SGZcW3wRjTDNr7VLcLypFfgSme8fV8m6Tyfe+\nLeP7FXeO5FnAu9baO4CncHti22f577u/tTYG1AJuw/07j8adWnCyMeaYTMa3jb/ty2mHvIk75JeV\n3rktnrtm1trfcaf9dDHGjMPNZ74CPjHGHOf1spdrrMaYBsaYfrhf2McYYy732nc4tyqXJMz7xat7\nF3/BHYc/07gTcyuDHkBNa+164HHcrvhTi4angPlAAncs/RLIeI9Yenz/8OI72Rizh7X2W2utBVK4\nPSXZmEibHt8TuMnDUcC5wF9xvwX+E/i3MeZyrzcgW/H9A/c5aozbg1OkDu6b+9d/vHm5S4/vMdzX\nWBPcb9EfW2sXec/Zv4Dvshzf47j7xM4FngbWAh95l+dkYSJ3AJgD/Ac3qQEYDnQ3xhwH4MX9Mu5r\nJNPS4xvqxbPOG977BPe1crkxppYxZq8sx3eDF9+qtA+ddrhz1zriJhOZfu/7w/OH27P5nJdUFO3w\n8l9gtwzGtbX4bvLaRgPNcb94Yq39zWvL9F7KW/vbbky7fn+gWhanEGzttTEaGIU7ZHqHN93hVuAg\n7/ry/t/7KxDFXfD2ATDaGNNoZ6YylPkTmTbMdJc3XwBr7VO4GerALHyglodJQEtjTBPvBTMNt8dp\nb2NMM9xJyBOBBdbaqypQfMcbY640xpwKXAHMstbOqQDxzQAKgXe8F9VPwAbgbmvtE15vQLbiW4O7\nmGEN7vN3q9d7eAYw1Vq7LsOxbS2+GYAF9gCuN8ZcBwwB5lprZ2c5vtW4W5ptADbhJrQtcRPu7yHj\n815iuO9F/wIO9r4xb8QdOh1ojDnWGHM87tDGLxmMa2vxtfZGEqCkp/0G4BrcXuRsTPHYVnx+b2it\nEe68zhHAr1mOr6Uxpqu3mu9nY0xbAGNMT9wvVd9UgPiOs9YW4A5B9jXGdPA+Q/fBfV1nK7biv60p\nmZf7KXCIMSYvS8PNWz53Rf97PYFzjTHVvL/t/rgJUblIGw7d3Xvs2V6P5iTgB9xe/h1WpknYFsNM\ny3CzxE7e1TfhzlXp5B2b7cm4f8YPuB96lwF4icxuuN+cz8RNes72JulXlPhqAN/iJjvNgKestdma\n97K1+Py43/IBwrhbXt2z9ZuXu209fwtxn8PGwJPW2ucqSHyzgKa4wyxn4PY8/dNam615JVuLbzfc\nRGxf3G/8z1lr/8+7PmM9JdbapLX2S9yeuHfwVm1aax/i/9u79xi56iqA499SpDxraUGh0jQocMAa\nwBeBJopoQEBSHipioigUNDwsIiJJtVbAmICFGsAaImglIqQWRFHSSkHRpLysyMPikUbAQiQiFLEp\nVrD4x++ODstuKXbu3Nvd7+efzdx7Z+fszOzkzO9xDnyTMiK7O3BmleD21SDxnV0dX1t9gd0LuJgy\n5fxAi+J7AXg3MI3yGn+8ek6bju/z1fF1wPERcQUwETilWsPWdHyd999cyjrEIyhrxM7MzEcbjq3z\n2j5fXbI9JQHq95fioeLrjNZ9lzIteRkQwOfq+N8YZDp0FWXA4JIoFQjGUz5D9oiIPTZEkD45AAAH\n6klEQVT0c63XvSPPAiZn5owqSzyO8o85MzMfjoiZwPuBb1O+pff9Q6RXIqKzgPLczFwcERcBC4E7\n2rAzY5D45lB2z/264dCAQeO7ELg5M1ux/XmI5+8nmfmrhkMDhozvpsy8teHQgPY/f1DqggGXAndT\n6qrdFy3aWdUV352UUeJ7ImJMZq5tODTgJfHdRSmdsRWwQ2be1mhgla74fgNcRSkftF0DU+CDGvD+\nuz4z74+I0dmCOlwD3ns/y8zfRrvKenTiW0bZzLWC8trWVtojSpHuoykbjV6bmSdG2Wl7KfA45Uvm\n9ZTRsRsy87Ehf1mXXo9GDTUNNqU6/zvKXO0Wm3ICBpBlF9UFwOERMQ+4MTNvb8sH+CDx/bQtCRgM\nGt9NbUnAYMjnrzUJxBDxtSIBg/Y/f5UngWcoo9fbQ3O7mYfQie84YCyUEbFGI3qpTnwfASZl5u/b\nkoBVOvF9mBLfk21JwCrd77/xUEZ7Go3of7rfe9tBM7uY16MT34eAnTNzXZ0JWGXgUoaDq6nkk4FL\nMvNCyus4kbJ8ZYP0eiRsR+A84KnM/FJ1bD5wdWbeHKUUwWOZ+deePWjDqnUQL7TsDfpfxrdxjG/j\ntDm+iAjK9MWiak1HqxjfxjG+/1+bY4Nm44tS1uZsYGpmHlYdOxw4ijLQ9IMsOzc3SM/bFr2aaaY2\nDf1LkiS9kgFT8ddSRr7GZ+ar3uxRS+/IiDiS0t7gNcCCLFuru8+PgtYN/UuSJK1XRGxLKV/0VuDU\njZmGr62B91DTEN0LD6MUanwbcEtmrmrLokRJkqTB9HI6tLYkbH2i9MU6llJccktg28w8ou+BSJIk\nNaTvSViVQc6nVNSeUh1bDpyUmUv7GowkSVJD6uwdufmA2++IiP0zMym9C1dFadAMpc3ANRHxgbri\nkSRJapOetxCKiF0oTYSvBVZWlfHHU9qCPBoRz2bm8oi4ADghSuPNeykVtuuu8yFJktQKva4Tth+l\nPMUkynqvw4DdMnNmREwGPkZpaXI1MIpSU+MOYHYTLSQkSZKa0uvpyD8Ds4BFwOmUqrYHRcTeVR+s\nRygl/48GdqL0WTqnk4BFxOgexyNJktRKPU3CMvOJzLyL0s9pb0rfqSspCRmUaceg1BD7e2ZeXpWm\n2Ky6v+UpJEnSiFBXsdbJwBnAOkqn8+9Q+i49Qukhd2/XtS+rmh8RewErM3N1z4OTJElqgTqLtR4K\nnAJ8A/gl8M5qlKxz/mUd2SNiHDATOBCYvqk3+ZYkSRpKz0tUdFoSUaYk7wCmA2M6CVhXy6KBCdg+\nwE3Ag8BUYEVnmlKSJGm46XmS05lazMwngcXAamDCwPOD+CNlxOxO4CTgi8C8iDi21zFKkiQ1rZaR\npogYExHvAt4ObAOsGuSaXSPiUxExFiAznwNuA2YAizNzFrAcOCYi9q0jTkmSpKbUkoRl5lrgEOB5\n4MTMXNN9vmru/QXgGODIrvstBi7JzEeqQzcAa4Dn6ohTkiSpKXWuuZqdmfMz8/lBzm0B3AcsAQ6I\niF07J6pq+rtVN99AGUn7R41xSpIk9V1fGnhHxJ6UUa8lwPLMXF0VZt2HsoNyeWbOra4dBZwHvBH4\nBbAoMx+rPUhJkqQ+qrNExajMfDEiTgHGAg9TSk9sk5mf7LpuBvAWYG5mPlgdmwRMzMw7awlOkiSp\nYXUtzB8FbFXdHEcZzVoAfBn4YEQc0nX5DymFXC+KiNMiYkxmrjQBkyRJw1kddcIOAC4G5kTEFMro\n12SAzHwKmA3M6brLaOD1wD3AVdWifkmSpGGtZ9OREbEt8BXgIWABcAUlsXoGOD0z96yuGwP8iNK4\n+/6I2AHY0nVfkiRpJOnlSNiLwOPAksxcBZwL7JeZlwEvRMRnq+smAH+g1AAjM/9mAiZJkkaazXv4\nu9YACzNzZdex26ufs4BDI+LrwLPAssz8dw8fW5IkaZPSsySsakfUnYBNpvSBhFIX7GvAjsDD1dow\nSZKkEauXI2ED7Qw8HRHXAGuBn2fmozU+niRJ0iajljphEbETsBS4H1iQmVf3/EEkSZI2YXWNhK0D\nrgTmWHJCkiTp5frStkiSJEkvVWcDb0mSJA3BJEySJKkBJmGSJEkNMAmTJElqgEmYJElSA+os1ipJ\njYmIqcBXgTcD1wPjgW2A+Zl53Svc9xPAezLzhNoDlTRiORImaVjKzKXA94A/ZeapmXkccDIwKyLO\n2IBfYf0eSbWyTpikYasa0fp0Zk7tOnYIcB1lhGwe8AAwAViWmZdHxG7At4CJwC3AjZl5c0R8Btgd\neA4YB5yZmWv6+gdJGlacjpQ00twNbA28jtLV4zaAiLg3In6cmSsi4vvAgZk5ozr3XmBaZh5c3T4f\nOAeY3chfIGlYMAmTNBKNoizHOCgiPkoZ3doeeBPwxCDXHwZMiIh51X0nAH/pU6yShimTMEkjzX7A\nauB9wL6ZeRRAROwLjF7P/W7PzNM6NyJi61qjlDTsuTBf0ogRETsBF1CmEScAT1fHNwN26br0n1QJ\nWUQcDyyijJptVh07CtiQxf2SNCQX5ksaliJif+B8YAqwkFKiYixwVWYujIhJwDXAQ5RkbBpwHzCd\nsmZsIbACuDUz50fEDGAqsBLYEjgrM//V379K0nBiEiZJktQApyMlSZIaYBImSZLUAJMwSZKkBpiE\nSZIkNcAkTJIkqQEmYZIkSQ0wCZMkSWqASZgkSVID/gMaOU9yX3bJPAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11e1f5bd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data[['SX5E', 'sigma**2', 'V_t']].plot(subplots=True,\n",
    "                                       color='blue',\n",
    "                                       figsize=(10, 8));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "h5 = pd.HDFStore('data/var_data.h5', 'a')\n",
    "h5['var_swap'] = data\n",
    "h5.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Variance vs. Volatility"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Squared Variations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Additivity in Time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "## function to calculate the realized variance\n",
    "rv = lambda ret_dat: 10000 * 252. / N * np.sum(ret_dat ** 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data = np.array([0.01, 0.02, 0.03, 0.04, 0.05])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N = len(data)\n",
    "N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2772.0000000000005"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rv(data[:2]) + rv(data[2:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2772.0000000000005"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rv(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data = pd.DataFrame(es['SX5E'][(es.index > '31-12-2012')\n",
    "                             & (es.index < '01-01-2014')])\n",
    "## we need log returns\n",
    "data['R_t'] = np.log(data['SX5E'] / data['SX5E'].shift(1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "98.3424775210876"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N = len(data) - 1\n",
    "N\n",
    "var_1st = rv(data['R_t'][data.index < '2013-07-01'])\n",
    "var_1st\n",
    "var_2nd = rv(data['R_t'][data.index > '2013-06-30']) \n",
    "var_2nd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "257.4914940719223"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "var_1st + var_2nd\n",
    "var_full = rv(data['R_t'])\n",
    "var_full"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16.04654149877544"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vol_1st = math.sqrt(rv(data['R_t'][data.index < '2013-07-01']))\n",
    "vol_1st\n",
    "vol_2nd = math.sqrt(rv(data['R_t'][data.index > '2013-06-30']))\n",
    "vol_2nd\n",
    "vol_1st + vol_2nd\n",
    "vol_full = math.sqrt(rv(data['R_t']))\n",
    "vol_full"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Static Hedges"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Broad Measure of Risk"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/tpq_logo.png\" alt=\"The Python Quants\" width=\"35%\" align=\"right\" border=\"0\"><br>\n",
    "\n",
    "<a href=\"http://tpq.io\" target=\"_blank\">http://tpq.io</a> | <a href=\"http://twitter.com/dyjh\" target=\"_blank\">@dyjh</a> | <a href=\"mailto:team@tpq.io\">team@tpq.io</a>\n",
    "\n",
    "**DX Analytics** |\n",
    "<a href=\"http://dx-analytics.com\">http://dx-analytics.com</a>\n",
    "\n",
    "**Quant Platform** |\n",
    "<a href=\"http://quant-platform.com\">http://quant-platform.com</a>\n",
    "\n",
    "**Python for Finance Books** |\n",
    "<a href=\"http://books.tpq.io\" target=\"_blank\">http://books.tpq.io</a>\n",
    "\n",
    "**Python for Finance Training** |\n",
    "<a href=\"http://training.tpq.io\" target=\"_blank\">http://training.tpq.io</a>"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [Root]",
   "language": "python",
   "name": "Python [Root]"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
